How far in advance can I prep the tomatoes for this recipe? (i.e. will I run into any problems if I leave the diced, salted tomatoes and basil sit...

I have done this. If you are really worried about them deteriorating, I have put them in a colander over a plate so the juices drain away.

I've definitely seen other raw chunky tomato sauces like this that leave the tomatoes out in the salt and herbs for a few hours, but if you're concerned (or think it might be longer) you can stick it in the fridge and let it come back down to room temp. (Allegedly refrigerating doesn't affect the flavor or texture much, as long as you don't eat them still-chilled!)

I've made this dish a few times and love it. In fact, thank you for reminding me. I haven't made it yet this year.

I did prep the tomatoes once just a couple of hours ahead of time (minus the basil) and I don't think it did the tomatoes any favors. They took on an almost canned tomato texture. It could have been the tomatoes themselves, but really, the time it takes to boil the water and cook the pasta seems like just the right amount of time to keep the tomatoes tasting wonderfully fresh.

The tomatoes will be fine--perhaps better, even-- but the basil will likely turn black. I'd prep the tomatoes and add the basil 10 minutes or so before finishing the dish.