Whenever I've tried to grill tofu (on a propane home grill), it falls apart and into the grill. Is there anything I can do beforehand to prevent the tofu from disintegrating, and get it to behave more like a hunk of meat?
Standard tips for browning/frying/grilling tofu;
The same advice applies for pan frying. I prefer to work at a high temperature, others have had very good results using only medium. Use a very thin, flat metal spatula to turn. Specific to the case of grilling, be mindful of the gap the tofu will stretch across on the grate; it may be crumbling because it isn't strong enough or thick enough to sustain wide gaps.
Additionally you can pre-bake the tofu to dry it out further. I have heard tell that salting lightly with finely ground sea salt helps prevent sticking but have no experience with this, and have had good results without the added sodium.
Typically the moisture in the surface of the bean curd is causing the sticking. Prevent or inhibit this and you should be good.
Bamboo skewers are popular here in China for tofu and mushroom grilling: seems to be the scraping of the spatula that disintegrates the tofu when it's time for flipping.
No need for super-firm either. Basically it's a size issue: the moister and heavier the thinner the slice and more it is 'woven' onto skewers. Rule of thumb if you can handle the piece without destroying it, probably will work on the grill.
If the grill spaces are very wide and sticking is still a sticky issue, then try creating a rack of foil to balance the skewers on each end so that tofu grills horizontally in air.