Pit beef was never a big deal among Baltimore Jews, especially the ones who keep kosher, but I don't see why not. The original version is a round roast, rubbed in seasonings and put on a charcoal grill turned on the grill until cooked rare, then sliced thinly and made in a sandwich on rye bread or a kaiser roll with horseradish and maybe some barbecue sauce. The only problem for the kosher consumer is that the round is from the hindquarters, and such cuts aren't available in kosher meat markets in the States. I would think one could use an alternative cut, but I'm not sure which.
The round is very lean, but can be tough. This is dealt with by (1) serving it rare, and (2) slicing it very thin.
Here are some of the alternative kosher cut's I've seen in the 7-mile market:
Rib roast -- I once found one on sale, and once you cut away the fat, it's really good, but it's also way too expensive for a proletarian local specialty like pit beef.
"Apple Roast" (what is this? It looks like it's farily lean and has an even grain, but how would it turn out is roasted rare and sliced thin?)
Any other cuts I should know about?