its jetted wrong, might be on the lean side

If it was running fine before you cleaned it but could not get the pilot out I would suspect you washed some  foreign material into the little holes of the pilot circuit.  Pull out the pilot and make sure its clean in all the small holes.  then make  sure that circuit and the air screw are clean.  Give everything a once over again and put it back together.....i

When you cleaned it the first time did you make any adjustments to the air screw.  Did you ever remove it to clean it behind it---if not, that could be a problem, if you did remove i,t did you note how it was adjusted (number of turns  backed out from lightly seated) and set it back to where it was..just my .02  but I am by no means a carb tuning guru.

Im not sure im following...lets take it a step at a time...If it ran good before.... and it does not run well now... and assuming you did nothing to float bowl adjustment than it...and assuming you did not change jet size of the pilot or main t as you indicated the than I would think that it would have to be some dirt in the passages if the carb as you indicated the jets were not plugged.   Did you use compressed air to gently blow through the circuits  of the carb or carb cleaner through the little red straw both work well.

OR,,,,

You have an air leak between the carb and cylinder

OR  and most likley..

You have your air screw out of adjustment.   I didnt clearly under stand your post...you said you adjusted it to where it would barely stay running???  You should have before ever doing an;ything with the air screw ....turn it inwards until it lightly stops turning ...WHILE COUNTING THE NUMBER OF TURNS IN UNTIL IT SEATS)  I interpret you did not do this....If you did, than just adjust it back where it was.  If you you did not than assuming the pilot jet is correct or close you need to turn it in all the way until it LIGHTLY stops.  Than back the air screw out around 1 1/2 turns.  Start your motor and run it warming it up then see if its better.

Now you should be close assuming the pilot jet is the correct size.  Now adjust your IDLE to where it runs at the desired idle rpm......Now go back to your air screw....with the engine warm and running at desired idle adjust it until you get the highest Rpm.....than if needed turn down idle if it idles too high.

This is where my expertise from memory ends.....IF the final adjustment of your air screw is something like more than 2 1/2 turns out or less than 3/4 out for peak rpm than your pilot jet is either rich or lean.  At that point I always forget and have to refer to a section on "how to jet your carb" and follow the instructions.

I am not an expert and have not even played one on tv.  This is just me trying to give you some suggestions.    Any real experts feel free to chime in and correct me if and where I ma;y be wrong.

In any event, good luck, and I hope this helps.