Your ignition timing may be too advanced. Is your oil too viscous? Is your engine a high-miler in need of a rebore? I don't think a new carburettor (expensive) will solve the problem.
Is the engine easier to kick-over and start when it's hot? Does it rev freely when it's started?
Sorry, there seem to be more questions than answers here!
this bike should have a auto valve compressor that is to aid atartingbut be warned the sr was a pig to start especially when hot but a tip is to stand on the pegs and s l o w l y turn the engine until its just past the compression stroke( it will be hard to turn over then it will go easy ) it then is up to you to give it a bootfull and kick it through a full swing this is an art perfected by old british bikers! if you think its tricky the xt was the same only more so as you were usually up to your eyes in mud!