I have a 1997 MZ 500 Saxon Tour for over a year now and I have had one persistent problem with it pretty much since I got it. Whenever the engine idles for about 15 seconds or more and I give it some throttle, it stutters as if it was starved of fuel or misfiring. Sometimes it picks up from the stutter, but sometimes the engine dies. If I gently give it throttle every couple seconds this doesn't happen. This means every time I stop at a traffic light I have to be really careful with the throttle and rev gently every couple seconds or I may stall when the green light comes on. I set the idle speed higher than normal to counteract that and it helps most of the time but it's not a proper fix.
The carburetor on this bike is the Dellorto PHF 34 GS. I have cleaned it multiple times and all jets should be free of clogs. The accelerator pump is set to only kick in at about 1/4 throttle. To change that I would need to buy a new throttle slide with a different pump cam profile, which would cost over £80. Is this the right way to fix it or could something else be wrong with the engine? I have also recently replaced the air filter and checked for vacuum leaks.