I recently read a Cycle World article and in it the author talked about the problems Bombardier encountered in developing direct injection such as,for example, crankcase overheating.The article also discusses how the injector(s?) are located in the transfer ports and are timed to the closing of the exhaust port.
This leads me into the new Ossa 300 enduro which apparently has DI, or more accurately, hybrid direct injection.It has transfer port injection, like the Bombardier,plus a crankcase injector which delivers a small amount of premix to the crankcase for lubrication and cooling.A compromise yes, and most things in life are a compromise, but a form of direct injection nonetheless.
So,it seems, we have a direct injected offroad 2T.

My apologies to Dirt Bike - the new Ossa is DI.