Here's another trick that might work - a notched exhaust port. On some two-strokes, like my Victa lawn mower, the exhaust port has an exhaust port where the center of the port has a 'channel' that opens way before the rest of the exhaust port.
This type of exhaust port is usually done to reduce the noise of the exhaust. It works well to keep not only the initial blast from the exhaust from making noise, but it also helps trap the incoming intake mixture.
In the first part of the exhaust cycle the pressure differential is the highest. It has been estimated that the first 10% of the exhaust port opening does most of the work in dropping the cylinder pressure. So, the 'channel' drops the pressure, and then the rest of the exhaust port opens and provides an easy flow when the transfers open.
It may be that an exhaust port where the center of the port opens, perhaps 1/2 of the port width (or more), drops the pressure and then the remainder of the exhaust port opens later to provide an easy flow of the transfer. That would likely help to reduce the short-circuiting in this jug.