115 Yamaha running rough

[sidelock]

My 1998 115 Yamaha has been bullet proof and hasn't failed me once yet although I'm the second owner and have only owned it for the last five years. It has just recently started running rough/shaking but ONLY does this between 1000 and 1200 RPM. and anything above or below that it runs perfectly fine and smooth. Had Bass Pro mechanic look at it and do a 34 point inspection but couldn't figure out what is causing it to shake. They removed, disassembled and cleaned the carbs, removed and inspected the reed plates, did a compression test 120 across all four cylinders and suggested I change the fuel pump due to a suspected weak diaphragm , which I have done. They switched carbs around as well as the coils to see if symptom persisted and it did. Told me they had 13 hours into diagnoses but only charged me $450 for four hours.
I don't know about the previous owner but I only run non ethanol fuel and religiously add ring free.
Has anyone experienced similar issues or can offer some advice/suggestions, I just don't want to bounce around from one mechanic to another throwing money away and not find out what the problem is.