If you have the testing capacity to test everyone before they race, you hold the race (with only those that test negative). Test everyone when they come to pick up their packets a few days before the race. If the testing capacity doesn't allow you to test everyone, then you don't hold the race or only hold it with the # of people you can test. Maybe you add a $50-100 surcharge as I imagine it's not going to be cheap to test all those people (although Covid-tests are supposed to be free).
A massive race like NY could potentially hold the race over two weekends if you can't test everyone in one week. If your limit is say 5,000 tests a day, you run the first 25,000 people on one weekend (The women's championship) and then do the next 25,000 the next weekend (The men's championship).
I'd also suggest requiring everyone to get tested at home before in the two weeks prior to them showing up.
Here in Maryland, getting tested before you travel to the race wouldn't be a problem. Even people with no symptoms can go to the fair grounds and get a free test for piece of mind. I know labcorps will send you a test that you can do at home.
Healthy people racing isn't dangerous. Sick people racing is.
LRC Update: The podcast is up here. Debate happens around 19:00