Oh here is so much troubleshooting lol
About any air leak ...etc.. you can test that with Fi tool, just watch MAP pressure value, it should be steady on idle like 35-45 (also observing rpm so you will now why pressure rise or drop) if you have steady rpm and your pressure change, that is indication for something!
You dont need to test ECU with multimetar like Ruffus write, you do all that with FI tool, dont waste time
Also tilt swtich is good according the FI tool!
About that black stuff on fuel filter, I dont think that make any issue because you have good pressure!
Conclude; ECU read all good value, so could be wrong handling through the software or my theory (read bellow)
O2 sensor cycling on idle is way how ECU preform injection timing however it need some time to start cycling you should put some rpm-s. Not cyclinging on idle can indicate air leak (you can test that observing MAP pressure or baby powder method), O2 sensor problem or ECU software problem, in my experience I encountered all three problems
I write you before... try play with throttle and observe O2 behaviour and report here...
Now I will write what I think what is the problem (my fameous theory), after read all post my conclusion is FUEL! I know first you gonna think it is premimu fuel must be good etc... However you have trouble with two identical scooter, identical hot start problem....and you said you feed them with 98 fuel, that could be a trick!
Well, we should look wider picture, EFI in DT300/50 is basic I would say primitive if we compare some other systems...
System lacks of auto-adjusting feature for fuel octane, so it can make trouble advancing ignition timing during start because of ignition map limitiation if you pour higher octain fuel. When engine is cold ECU advance igntion more then hot, that is why you dont have a problem, however that changes when engine is warm, there is no need for too much advanced igntion and ECU retard it and makes trouble beacause of fuel resistance (bigger preigntion time). What I wanna said, iginition map is fixed and adjusting for higher octain fuel is not possbile so you should remove all the fuel and put 95 octain fuel, start engine leave it work some time to clean all remain fuel, get some rpm-s (I assume you cant drive because it is not in one piece) and test hot start. Maybe is "shot in the dark BUT" like Crossbolt write, but for sure you would not be the first with such a problem related with fuel octane. There are not many "cases" related with octain value but they exist and main problem is engine starting not performance so give it a shoot you gone loose few Eur on fuel