What can I substitute for dairy products in kosher meat dishes?

In the Israeli Army I've had a veal "parmesan" made with a tahini sauce. It's a very different dish, of course. It's also common to get beef/noodle recipes that don't include the dairy component.

In general you're often better off substituting the meat (for fish, or a vegetarian patty like seitan) or working off of different recipes. Trying to make kosher cheeseburgers (and putting margarine on the shabbat table) are the hallmarks of the newly religious.

In regard to the issues you've had with the Toffutti Sour Supreme...wait until you take it off the heat and stir it in right before serving.

If it still breaks, then try stirring arrowroot powder, tapioca starch (avail. in Asian markets), or potato starch (about a tablespoon per cup of sour supreme) into it before adding to the stroganoff. These starches (amylopectin) have a lower gellation point than grain-based starches (flour, corn, rice) which are higher in amylose and require heating to a higher temperature for the starch granules to swell and pop, releasing their starch.

OR

Try this recipe for kosher beef stroganoff where they're using coconut milk for the kosher cream sauce and say that the coconut flavor doesn't come through in the finished dish.

First ask yourself if the Dairy Ingredient is significant to the dish, some dishes can go without the dairy item. Olive oil for butter is the easiest example. I make Beef Stroganoff often, and I always put sour cream as an optional ingredient - garnish. My brother is lactose intolerant and he loves Stroganoff. Also, review some Kosher cook books, Joan Nathan comes to mind. Vegetarian cookbooks often have intriguing substitutions for animal proteins

It really depends what you are trying to do with the dairy. Is it for taste, consistency, moisture?

I keep kosher and often see recipes with dairy products.

If its baking often cream can be substituted with non-dairy coffee creamer or unwipped whip cream and butter can often be substituted with margarine of vegetable shortening.

For making a tempura batter just put water instead of milk.

I make corn bread (to be eaten with meat) and I use part soy milk and part mayonnaise to substitute butter milk. In the case of corn bread the butter milks main objective is moisture thus the mayo.

Anyway it is individual and like @spolsky said just don't try to make a cheese burger and never! touch things like vegetarian pepperoni! (just ask anyone who did)

I've had some luck with rice or almond milk, although you may need to also address technique. Stroganoff, for example, might require you to prep the sauce over different heat. I'd recommend flipping through a few vegan cookbooks to see if there's any analogous recipes that you could steal a preparation technique from.

BTW - I'm not super familiar with Kosher food prep, but does "dairy" include all animal milks (such as sheep or goat?) Does "dairy" also encompass yogurts, kefir, etc?

Beware most soy milk and almond milk is Dairy - they have milk in them or milk by products!!!!!