It's definitely worth pulling the diaphragm cover from the side of the carb and inspecting. It gets ignored for long periods and may be difficult to get off - I had to remove the carb and use an impact driver the first time.
The diaphragm must be clean and have NO cracks or holes. If it can't hold a vacuum, it cant work.
The plunger attached to the diaphragm needs to perform reasonably well as an on/off valve for the enrichment circuit - so it should be clean and show no more than mild signs of wear.
The cover has a very small drilling to connect the vacuum side of the diaphragm to the engine side of the carb throat. This has to be as small as possible to damp out pressure pulsing, but that makes it prone to blockage. Don't use wire or anything hard to clean it - I use copious blasts of CRC carb cleaner.
If when you took it apart it was pretty ugly, after reassembly you may have to re-tune your idle circuit/air screw as this may have been set wrong to compensate for the enrichment circuit not working properly.
The suggestion about redcing the diaphragm spring tension might be worth considering, but I think all that'll do is shift the point of snap crackle and pop to a lower rev range.
I had an old Ducati Pantah for years and to try and keep the *%#$#* Dellorto's in tune I spent a fair bit of time riding around with vacuum guages taped to the tank. That showed there's three basic states happening in the carb:
- Idle
- throttle-on
- throttle-off
At idle the throttle's barely open and the idle circuit controls mixture strength. There's big pressure-pulsing in the carb making the air pass back and forth through the throttle, so gas is sucked twice and a correctly tuned idle circuit actually delivers a "lean" amount of gas for each suck.
During throttle-on there's lower vacuum and reduced pressure pulsing at the throttle, and the idle circuit is less important because other jets/circuits come into play.
During throttle-off the throttle's barely open and the idle circuit is again the major player. But now, while there's high vacuum at the throttle, there's little pressure pulsing and gas only gets sucked once. A correctly tuned idle circuit will be delivering a hugely lean mixture until revs drop back close to idle.
Hence the enrichment circuit - which gets pulled open by the high vacuumof throttle-off and closes again when revs drop closer to the point where the idle state returns.
Softening the diaphragm spring will keep the enrichment circuit open longer, but there's a risk the circuit may be held open when you don't want it.