81 KZ250 Single (again) Runs, but stalls on throttling

Thanks to all you guys on here (especially in my last thread - KZ250 C 81' Single, fuel pours out carb overflow after rebuild) I've now got my bike RUNNING!!!!!!!

- The current problem is that even if I let it warm up, it stalls as soon as I try to move the throttle or apply any choke.

The float height was set by eye based on another spare carb that I had for parts that came off a running bike (I just figured it was worth a go as although it was sold for spares, I thought the float height was probably correct).

I've got a Pod filter on the carb and jetting is standard. (I know this won't be ideal long term) but I figured I should be able to get acceleration without stalling before I worry about re-jetting?

The bike idles, but the sound of the engine is like a wave going in and out slowly (if that means anything), so it revs normally then dies slightly like it's going to stall, then revs back up again to a normal turnover, then dies slightly etc. It never stalls unless I use throttle and it's not over-revving, but it doesn't idle consistantly. I've checked the pod filter and engine manifold are secured, so no air is getting in where it shouldn't.

There's one idle screw on the side, that when you screw it in, just stops the throttle from fully returning to the default position. That's screwed all the way out so it doesn't stop the throttle from fully returning in anyway. (I did test screwing it in a bit, but a little made no difference and a lot just caused it to stall)

It's 4 stroke, so I'm guessing there's no mixture screw to play with (sorry if that's a bit of a thick comment).

As always, any help would be most appreciated.

By the way you describe the idle it sounds like you may have a pinhole in the diaphragm in you carb and it is moving up and down as it is running. It should be easy enough to see by looking into the bore of the carb as it is running, even if you have to use a mirror to see it better.
Have you checked your rubber manifold for air leaks? You can spray it with carb cleaner as it is running to see if it changes the idle.