Why do you reject negative utilitarianism?

Therefore, it is a straw man argument that NUs don’t value life or positive states, because NUs value them instrumentally, which may translate into substantial practical efforts to protect them (compared even with someone who claims to be terminally motivated by them).

By my understanding, a universe with no conscious experiences is the best possible universe by ANU (though there are other equally good universes as well). Would you agree with that?

If so, that's a strong reason for me to reject it. I want my ethical theory to say that a universe with positive conscious experiences is strictly better than one with no conscious experiences.

What have you read about it that has caused you to stop considering it, or to overlook it from the start?

This response seems unlikely to be a crux for you, but I don't often see it written explicitly, so I'll mention it anyway in case someone reading hasn't thought of it:

Negative utilitarianism implies that you would prefer to destroy a universe with an unbounded amount of certain positive experience, if that would prevent an infinitesimal chance of one speck of dust getting in someone's eye.

This means that a negative utilitarian will basically always prefer that the universe is destroyed, since there will always (I suspect) be uncertainty about which things suffer (1 is not a probability).

1. Most women go through extreme pain during childbirth but nevertheless do this through choice and presumably think their life worth living given the upsides of having children. This must be irrational on your view.

2. Epistemic modesty - if negative utilitarianism is a plausible view, it is extremely surprising that more professional moral philosophers don't believe it. You can find substantial support for pretty much any view out there, including some very implausible ones, but I struggle to think of many genuine negative utilitarians working today.

When I know someone closely, I value their life and experiences, intrinsically. I don't feel as if I wish they had never been born, nor do I wish to kill them.

And it's straightforward to presume that, with people who I don't know closely, I would feel similarly about them if I knew them well.

So if I want to treat people consistently with my basic inclinations, I should not be NU towards them.

Toby Ord gives a good summary of a range of arguments against negative utilitarianism here.

Personally, I think that valuing positive experiences instrumentally is insufficient, given that the future has the potential to be fantastic.

It sounds like you're describing negative hedonistic utilitarianism, specifically. Although I would describe myself as suffering-focused and leaning towards negative consequentialism, I have two main points of disagreement with negative hedonistic utilitarianism, and a third which I've only thought a little about:

1. Hedonism. I wouldn't get into Nozick's experience machine or subject myself to wireheading (except for altruistic reasons), i.e. I see no reason to seek pleasure for its own sake like this or have my preferences satisfied by illusions. I think it's for these reasons that I've never really used psychoactive substances, including even caffeine and alcohol (I don't think people who do are doing anything wrong; they just have different preferences, and I do want their preferences to be satisfied).

I haven't seen a convincing case for hedonism, but I also haven't been looking much, so this could of course just be my ignorance. I think preferences are a more pluralistic value, and they could allow individuals to make the kinds of trade-offs in their own lives that they themselves would like to make. Arguments against NU for not respecting preferences can often be extended to arguments against hedonism, generally. So, for now, I lean mostly towards negative preference consequentialism, but not specifically negative preference utilitarianism (NPU).

Also, some of the major impossibility theorems in population ethics don't apply to negative preference consequentialism, precisely because positive welfare is impossible. You might say the same about NU (instead of just assigning it no value), but the asymmetry in valuing suffering but not pleasure is harder to justify than the treatment of a satisfied preference as no better than its absence, since preferences seem to have value conditional upon their existence. It seems silly to induce preferences in others just to satisfy them. For example, I convince you to really want a hotdog, and then give you a hotdog. Are you better off? I'd say no. I think convincing someone to no longer prefer something they had preferred before may be good. On the other hand, convincing someone their preferences have been satisfied when they haven't in reality also seems off, and the experience machine could also do this.

Peter Singer was a negative preference utilitarian for most of his career, but is now closer to a classical utilitarian, from my understanding.

I'm not sure whether a preference should be experienced as satisfied or frustrated for it to matter, but I do lean weakly towards yes, since I lean towards empty individualism (basically each experience should be considered a separate individual) by default and I don't think we should be concerned with trying to satisfy the preferences of the long dead (if they won't come back to life).

Btw, under empty individualism, if they can justify the procreation asymmetry (that an individual would have a bad existence is a reason to not bring them into existence, and that an individual would have a good existence is not a reason to bring them into existence), a negative utilitarian would be justified in valuing suffering but not pleasure, because experiences of suffering would be bad existences which are bad to bring about, while experiences of pleasure would be "good" existences, to which we're indifferent.

2. Aggregation by summation of independent terms. There are arguments for it (independence/separability axioms, Harsanyi's utilitarian theorem), but I think personal and interpersonal trade-offs should be treated differently in order to prioritize the worst off, and prioritize them more than summation allows without introducing discontinuities. Erik Carlson's Moderate Trade-off Theory is a bit closer to where I lean now. This is how it's defined:

Choose $r,0<r<1$ , and for each outcome, rank the utilities of each individual (perhaps after first aggregating utilities within each individual) in increasing (nondecreasing) order $u_1,u_2,\dots ,u_n$. Choose the outcome which maximizes

Since I do lean towards empty individualism, all trade-offs would actually be interpersonal, though.

3. That the order of events in time doesn't matter. I also suspect that for personal trade-offs specifically, the order of events does matter in a way that the major consequentialist theories don't usually allow, AFAIK. I think, with valuing preferences inherently, this could best explain aversion to get into the experience machine and the importance of consent, which consequentialist theories tend to only value instrumentally. I haven't thought much about what such a theory could look like, though.

(I'm not very sympathetic to rights-based theories; I think it makes sense to violate the rights of some to protect the rights of others, and the order in which this happens shouldn't matter, since it isn't a question of paternalism but of trade-offs between people. Also, the only right I would recognize is to preference satisfaction.)

Under empty individualism again, though, order would have to matter for interpersonal tradeoffs, too, for this to mean much.

A Buddhist-inspired answer would be that a classic utilitarian's craving for or grasping after pleasant or "heavenly" states of existence is what causes them to reject NU or at least not be negative leaning. With modern lexicon, that may be likened to a brain's reward function being why they reject NU, with pleasure holding more motivational salience than pain/aversion or tranquility (if the most latter can be attained or sustained).

What is the most extreme form of suffering that you’ve experienced and believe can be “outweighed” by positive experiences?

Partially torn/Extremely injured Wrist TFCCs and later what was likely CFS or some error in steroid hormone metabolism. I would not say that either of these were ever outweighed by positive experiences. With sufficient experiences of suffering, I became an NU and no longer desire (nor do I oppose) higher gradients of bliss, unless they work in some instrumental anti-suffering fashion.