To try to answer my own question, ASA doesn't look promising.

The following study doesn't support the use of aspirin in the outpatient setting to reduce [blood clots] associated with symptomatic but stable SARS-CoV-2 infection.

JAMA. 2021;326(17):1703-1712. doi:10.1001/jama.2021.17272 Effect of Antithrombotic Therapy on Clinical Outcomes in Outpatients With Clinically Stable Symptomatic COVID-19 -The ACTIV-4B Randomized Clinical Trial