Not too sure about barbecue techniques but if you can cook in a pot on a barbecue, then something based on the Greek (casserole style) Stifado recipe might be worth a try.
Stifado is usually made with beef (or traditionally rabbit) and has small onions like shallots in it.
The gravy/sauce is tomatoes and spices (it is quiet difficult to work out which ones, as each Greek island and even restaurant seems to have their own version of the dish.
If you can get the cooking time long and slow on the barbecue as with a casserole style cooking (I usually make my version in a slow cooker) the meat soaks up the flavours of the sweet shallot onions, the tomatoes and the spices.