In my non expert opinion it sounds like you have a link/sync or mixture problem. First check the basics.
All carbs should be operating in sync, from idle up until a point around 1/4 throttle or something the position of the internal butterflies should not change (in that first part of the throttle range it's all done by spark advance, the trigger turns under the flywheel).. After about 1/4 throttle then the carbs come into play. There's a lot more than can be done here but I'm just explaining a quick sanity check incase something is way off.
If the above looks about right then most likely I think you've got your mixture wrong on the low speed jets. When rebuilding the carbs did you set them? They should have come out for cleaning for sure. After a rebuild, when it's time to adjust the jets, it's totally normal for an engine to run seemingly perfect at idle and lower speeds but not well at all at different speeds underway. The simple thing is to start how the book says (believe it's 1.5 turns out but I always go 1/4 over that so 1.75 turns out - good to count how many turns they are set at currently first)..
The book may tell you to start the engine and go through a process of turning them in all the way until you note a problem, then back out until you note a problem, etc.. I start a little richer than where they tell you to and if the engine runs OK I start testing on the water, with the error always placed on the rich side of adjustment.
My way (not necessarily the right way) - start engine up and get the idle adjusted right (you will likely need to mess with the idle as you make mixture adjustments).. If it will idle OK without "loading up" and stalling itself out then it's probably not too rich (it will idle OK at first, smoke alot, then slowly die out with wet/fouled plugs), otherwise go in 1/4 turn on each carb and check result until it seems sane. Slowly push throttle forward, if you get a bog then bring each screw out 1/4 and repeat, if it's loading up at idle go in with the screws. Eventually you get it about right - then after 5-10 hours of use, pull the plugs and read how the individual cylinders are doing (if one is lean bring the screw out a bit).
Jon