How can I marinate meatballs without making them "mushy"?
I would crispen the outside a bit by frying or baking them first. To improve the outer crust, you might dust with flour and corn starch before frying. Typically I have not previously had problems with meat balls in sauce becoming mushy using minimally breaded mix, spices, and lean -ish (90%) ground meat. Here are some additional points to consider;


If you use bread in your meatball mix, you might tilt the ratio more in favor of the meat
If you are not using egg or some other binder, you might try doing so to create a tighter bond inside the ball
If you are cooking the sauce at too high a heat (I normally have mine set as low as possible when doing a long cook) it may come to a simmer, making the sauce likelier to disrupt the meatballs. Maintain a lower heat or use a heavier pot
If you are using ground meat, there is more room for the sauce to creep in. Make sure that they are packed sufficiently tightly when rolling them


Short of leaving the sauce and meat overnight, flavors will transfer more quickly in warmer temperatures. I am having trouble locating definitive resources to back this claim up, so I am speaking mainly from experience. However, one caveat exists particular to collagen and connective tissues in meat; here it is explaining why stews and other foods taste better the next day. Mixing water and strong acids is an exothermic process (gives off heat, does not benefit from warmth). However, this process is about mixing strong acids and fats. I would also mention that you are supposed to store tomatoes at room temp as the cold does not preserve their flavor and inhibits ripening, though I'm not sure this is relevant.