Aye srx ijk, welcome to the madhouse!!
May I ask if your machine is the twin shock or the mono and what year and CC's?
My first thoughts are, have you renewed/cleaned the air filter? And, what colour is the plug?
Ian's AMAL carb advice could apply, as it is the slide carb part of the instrument that is controlling the engine running up to half throttle, when the CV side starts to take over.
I have both a twin shock 1986 1JK 600 and a 1991 SRX 400, with a 1991 XT600E motor installed and both are using the standard slide/CV carb.
Also check that your choke plunger mechanism is not seized and the little rubber seal in the end of the choke plunger is in good condition, or else you will get bottom end fuelling problems, as you describe.
It's part #46 in this fiche image of the carbie on the Fowlers (Bristol) website. Link:
SRX600-1xl-1987-999-a/carburetorThe price is pretty eyewatering!
So try NRP-carbs, they supply spares in good quality viton that withstands the E5 and E10 fuels Link:
NRP-carbsWhilst you are under the tank check all of the fuel hoses for cracking perishing as either E5 or E10 will destroy non-VITON fuel pipes and if they leak it's going to be all over a hot engine, with no way of getting to the fuel tap on the underside of the tank!
I was lucky and found that mine had perished, so was able to replace them, without incident. However, I had a small grain of muck hold the float needle open after a 60 mile canter up the A9. When I stopped at some temporary traffic lights the carb overflowed onto the running engine and the hot exhaust and the bike and I were enveloped in petrol vapour! Luckily, the vapour didn't ignite and turning the engine 'OFF' shut the vacuum fuel tap and stopped the flow of fuel. It could have been different if I had left the fuel tap in the 'PRIME' position.
Do you have a workshop manual for the machine? If not, please PM me, with your email address and I can forward you a *.pdf file of the manual.
I hope that this helps you find the gremlin and SteveL, SteveH and IanR may all chip in with their pennysworth.
Good health, Bill