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.

American's Test Kitchen recently had an episode on the topic of spaghetti and meatballs:

http://www.americastestkitchen.com/video/?&docid=36514

Their trick was to first bake them in the oven at 425F for thirty minutes, make the sauce separately, and then put the pot (with the sauce and meatballs) in the oven for another hour.

You instead of having to do something "for several hours", the entire process takes around ninety minutes. Haven't tried it myself yet, so YMMV.

I don't think that's the cooking time which makes your meatballs mushy, especially if you keep them on the stove for long time. My guess is that the composition of your meatballs contain too much bread. Also the kind of bread is important. Always prefer using small bites of the soft part of the bread instead of breadcrumbs. Eggs are also important (did you use them?) Try this:

• 70% meat
• 30% bread bites mixed with eggs (let's say one egg for 5-7 meatballs)
• Salt, garlic and whatever you like

Mix everything for 5 minutes (just use your hands) and I'm pretty sure the result will be great.