I don't really understand what would change with port overlap /timing with a turbo. I think the biggest challenge is to get the exhaust energy work both the resonance pipe AND the turbo. The way I always understood, exhaust pulses have basically 2 waves of energy. First is more or less the pressure left over from the bang, the rest is the piston blowing stuff out. And I think the first has the most energy by far. That is basically why one can make 2 bar turbo pressure while the pressure in exhaust is only 0,5 bar or so. The energy the turbine consumes is for a great deal kinetic, right?
So I think it will be a trade off. Both the resonance pipe AND the turbo need energy to do their thing. And for the carb. Either before the turbo having mixture though the carb, or after the turbo but then your fuel float bowl will have to cope with the turbo pressure, and the fuel pressure needs to be turbo pressure + 0,2, and you need a big ass jet in the carb. And you will probably blow all seals in the carb. It will be very hard to get it right and get more power compared to an well tuned pipe. The turbo might mess up the pipe more then it can bring to the table. A well tuned pipe could be considered as an kinetic energy re-use charger devise.
I think this is basically why Rotax did what they did. And 4 pound of boost is near to nothing. Just enough to compensate for the elevation. Their turbo will not consume much energy relative.
I know the R5 turbo had blow though carbs, while the R5 alpine turbo had a suck though before the turbo. My knowledge is from that era, so don't kill me if I'm wrong.
Always loved this gif, that tells what a well tuned pipe does better than 100 words can: