Did you do basic carb setup? It sounds to me like the carb rack is completely desynchronized. Especially if engine is slowing down after being revved in extremely lazy fashion.
I've just fixed it and taken her for the first proper run in I can't remember how long. I am so ridiculously happy to be mobile again!
The problem was the new fuel line was pushing against the throttle adjuster on the carbs, which meant the throttle cable was taut enough to be engaged as if the throttle itself was about a quarter turn. I had an inkling this was the reason and when I turned the handlebars the engine would rev higher turning it to the right and then drop when I turned it to the left, which backed up the theory. I just took the tank off, loosened the throttle adjuster nut to give more play on the cable and after putting her back together I got the expected stalling when trying to start her. Put the idle adjuster screw back in, set it midway and after some tinkering got the idle down to around fifteen hundred. She is running almost perfectly for the first time since I got her and after taking her for a spin to charge the battery now starts on the button first time. I'll see how she starts tomorrow from cold, but I'm hopeful I might have finally sorted out that particular problem.
I'm guessing a little, but the airbox and filter are not just there to stop crap getting in the engine but also to regulate just how much air is getting to the carbs. A leaky airbox can't control the airflow effectively across the range, so you get all manner of weird problems happening. I also replaced the petcock because the previous owner had chopped the filters on the old one and put in an inline filter in the fuel-line instead. That actually ran uphill, so I think the flow of fuel to the carbs was also causing problems, probably because it was only trickling down to the carbs.
I'm going to see what the mpg is like over the next couple of weeks before deciding if I want to rebuild the carbs just yet. I've got a hundred other things to sort out (no headlights, no indicators, retainer missing from rear wheel, no rear brake...) and at least with an engine that runs my time might be better spent sorting those out before taking her off the road for a few weeks to clean up the engine itself. I just want to be able to ride in truth, I don't drive so the bike is my only means of transport and it sucks when I can't wander into town for weeks and months at a time (I live in the middle of nowhere).
I know at some point I'll have to rebuild the carbs and swap out some parts, maybe the needle or main jet because the idle screw is turned out a lot further than it should be to get the bike idling at a reasonable rpm (if I turn it fully in she idles almost on the redline!), but I'm not overly concerned right this minute to start playing with it.