Where do the compressed gasses of a charged engine goes?
As long as the rpm is kept up, the charge coming out of the compressor has quite a bit of inertial mass and is more or less flowing continuously even though there is a valve downstream opening and closing.  There will be a pressure and velocity fluctuation near the valve as the charge just upstream is admitted to the cylinder, then cut off.  But because the opening and closing is happening so fast, these fluctuations taper off up stream.

This is one reason for having long intake runners on a 4 stroke; to take advantage of the inertial mass of the long cylinder of air in the intake duct.  On a non-supercharged engine, this helps with the preliminary filling the cylinder during the intake stroke because the piston doesn't actually have to "suck" initially.  As the intake valve opens, air comes rushing in pushed along by the inertial mass of all the air back up the intake duct, like a crowd of school kids jamming up in the hallway and piling out the door when it's opened at the end of school.  The ones closest to the door don't have to be pulled out; they are pushed out by their mates behind.

Anyway, the main issue is managing the intake charge and its inertial effects, and the increasing difficulty in doing this at lower speeds or idling.  I would expect you would have to do a lot of experimentation with compressor gearing/speeds and intake runner length trying to get an engine to run smoothly across the full operating range.

Your project sounds like a variation of a 2 stroke diesel, which doesn't use crankcase pressure to drive air into the cylinder like a spark ignition 2 stoke, and therefore requires a supercharger or turbocharger compressor to push the charge along in the absence of a 4 stroke's intake stroke to pull air in.  Possibly looking into 2 stroke diesels would help.

I'd also look into using an electrically driven supercharger in your design which would make it easy to experiment with different speeds and could really improve operation over the speed range by using a computer to manage it.