All in trying to help.
pulling off needles and mains...
Idle, pilot circuits are plugged somewhere, the choke or a leaking float valve lets it start, and if you get lucky it grabs enough air to lift the slides a bit so gas can flow though the main jet, taper needle, then it revs, try to idle back, no fuel, it dies. Have you read the carb guide? look up in the tech section read the guide till your eyes bleed THEN go back to your carbs. I smell that maybe someone did a dip type cleaning of the carbs but never really pulled cleaned all the jet passages etc. You ask if the carbs have any adjustment screws??????
BS34s have an idle fuel screw top front, from the factory it's covered with a brass plug. If the plug is still in, the carbs have NOT been "cleaned".
Here's a bit of a riff; you are asking for expert advise (sic) but you haven't done leg work 101, search and read threads containing BS34 every conceivable issue with a BS34 has been detailed to death on here with super detailed pics with arrows, pointers and a detailed description (Alice) . You get familiar with the basics, do the recommended fixes, then if you still are having issues start asking questions detailing what you have done so far, so we don't have to play 64 questions.
One of these days we should do a BS34 specific overhaul thread. It would help the newbies (IF they read, follow it, LOL).
possible BS34 carb issues.
plugged; idle, pilot, choke orifice.
Leaking float valve, or it's oring. plugged float valve screen, mis-set float. leaking vacuum line, intake manifold(s)
bad petcock diaphram,
Usually it's several of these. Fix one issue and the other problems make it run worse, the leaking float valve lets it run with a plugged idle circuit, fun ensues till everything is right. LOL.
Get that all fixed and you still need to do the washer mod to get rid of hte off idle flat spot.
Then there's throttle shaft seals.
I have been through at least 10 sets of BS34's I budget about 5 hours to get a set right, I know all the tricks and short cuts, have a dedicated carb bench and a bunch of special tools made. All that said I am no carb expert there are others on here that are lot sharper than me. You CAN do good job on your carbs, BS34's work great when they are right, but it's not a quickie thing