I'm a noob with tw's myself but have been riding and working on bikes for myself and customers for a while.
It sounds to me your coasting enricher diaphragm is causing issues (link for some reading - How a carburetor works: Carbs explained - Ninja250Wiki), as that explains as well as I could.
did this happen after you cleaned the carbs? Carb cleaner is known for fucking with rubber, so it may have cracks in it, or it may have previously anyways. I haven't had my carb open yet, but the diaphgram should be part #17 here:
I'd start by inspecting that, as they're like $20 (i'm sure cheaper options) and for how cheap i'd probably also replace the spring.
The passageway there may be clogged too, use some compressed air (not much pressure) and see if the flow seems good.
I'd spray some brake cleaner or engine degreaser on the engine, then some gold bold, or other powder all over it once it dries. then run it. if its leaking oil it should leave a trail where its leaking from.
valves should be checked at 600 miles, then every 3k after that, if you don't know when they've been done, i'd do them, its easy and they're probably within spec.
most motorcycles wear 2:1 ratio, rear:front, not sure why the tw would be any different, but street legal knobbies are new to me (esp this size). I put some sr428s just on myself so we'll see.