Medicine isn't my area, but I'd guess the timelines for vaccine trial completion might be significantly accelerated if some trial participants agreed to be deliberately exposed to SARS-CoV-2, rather than getting data by waiting for participants to get exposed on their own. This practice is known as a "human challenge trial" (HCT), and is occasionally used to get rapid proof-of-concept on vaccines. Using live, wild-type SARS-CoV-2 on fully informed volunteers could possibly provide valuable enough data to reduce the expected development time of the vaccine by several weeks, with a large expected number of lives saved as a result.
Similar usage of HCT's seems to generally be permitted by the relevant ethics committees for low-risk diseases, such as dengue fever, but not high-risk ones, like Ebola or HIV. A brief look at a WHO document on these, and a longer look at relevant US federal law, didn't turn up any hard rules on how dangerous a disease can be before exposure to a "wild-type" virus is forbidden, and both at least mention considering societal benefits as a factor. However, sometimes HCT's for relatively minor diseases like Zika are refused.
The WHO document mentions that these sorts of tests are considered better for selecting between vaccine candidates or supporting evidence than as robust proof of effectiveness for general usage (see Section 5 of the linked document). The document seems to expect that most usages for preventing dangerous diseases will involve modified diseases. Using wild-type coronavirus would be both faster and stronger evidence of efficacy.
There are probably many other people on this forum who could address the expected value of such a trial better than I could, but my suggestion is that EA's engage with the relevant regulators to push for allowing such trials to take place if they would help. Basically, having volunteers put themselves at risk for a faster vaccine would be net positive; independent ethics committees might reject such a study anyways; generating regulatory or public support could make this less likely.
If this were to happen, it seems like a key narrative point would be that the government is allowing people to voluntarily take on risks to find a cure. I think that there would be plenty of volunteers if you asked right, and if some EA's were to do this, it would help their optics tremendously if several of them vocally volunteered.
If it were possible to make a home test kit for COVID, I think that would be helpful. By home test kit I mean an arrangement where people could order these tests by phone or from Internet and they would be mailed to them. Then the person would proceed to take a test sample according to the instructions in the kit and mail it back to the laboratory. The laboratory would test the sample and give the person the results via phone or web.
This kind of arrangement would allow people suspecting that they might have COVID to self-quarantine until they have a certainty (or near certainty since no test is perfect) whether they have the disease or not. Thus, it would lead to less people being exposed to potential early-stage COVID carriers and hinder the disease from spreading. Importantly, it would also protect the health care workers as they would have to come to contact with so many potential COVID carriers.
You might be interested in the Just One Giant Lab OpenCovid19 project. They just had their first conference call and their goal is to "develop an open source methodology to safely test for the presence of SARS-CoV-2 using tools as common as possible".