I thought an extra tooth on the front was more for lower revs at higher speeds?
Sorting problems is all about using a logical process of elimination. (or you could just put your problem on the foc-u facebook page and have a million random people just take a punt)
If it's easy to do, why not stick your old sprocket back on and see if the problem goes away? You may have introduced a slight inertia mismatch (google that - it's a bit of a black art I've never totally got my head around)
If you still have the problem you'll need to look a bit deeper.
Is your 'see-saw' acceleration connected to the throttle position (on/off) or does it also happen mid-position and in the middle of the rev range and in the higher gears?
It sounds weird, but I've had my front caliper seize over winter, when riding, the bike will accelerate and lift the front wheel but on closing the throttle the front end would dive and bike felt like it was dying? Is it all spinning freely up front?
What is the issue with gears 1 and 2? I assume it feels sloppy in the gear lever. check the pedal linkage and if you have the sprocket cover off see if there is any play in the shaft.
With the bike on the side stand you can also remove the clutch cover and see the gear shaft turning the drum on the right hand side of the bike. you can get wear and/or bending on this end of the shaft which can cause issues. Also while you've got the clutch cover off you'll see the small amount of play in the clutch.
I can't see how there can be any elements of slack in the gearbox? There is a small amount in the clutch, a little in the chain. Check your sprocket nut isn't coming off.
The bearing in the gearbox could be failing, but I think you would know about it as it would make a noise and or leak oil.
Take the sprocket cover off, Get it on the centre stand and turn the back wheel backwards and forwards see what is moving.