Okay, you're not going to get that much benefit from a manifold style injector like you're discribing. Especially if you're injecting premix.
Here's how Rotax does it with their E-600: Fresh air is aspirated into the cylinder instead of fuel/air/oil mix, it's scavenged up through the transfers, and as soon as the exhaust port closes, the fuel is injected directly into the cylinder.
A seperate injector keeps the crank bearings, big end bearing, and wrist pin lubricated directly. And because gasoline vapor isn't moving through the crank case, less oil can be used because it isn't being dissolved and stripped off surfaces.
Furthermore, because fresh air is scavenging the cylinder, higher peak crankcase pressures can be used without sending massive amounts of unburnt charge out the pipe. This brings emissions down while improving power/economy. This large amount of charge cools the cylinder and piston better than a smaller charge, and gives more energy for the pipe to rebound.
And finally, no waiting for fresh charge to flush the cylinder when starting. Direct injected 2 strokes start up on the first pull.
