If it is runing (you say it will at higher rpm of 2000) -- I would run a few tanks of gas with Sea Foam added and see what happens.
Example --- Bought a used 500 Ninja with 1000 miles on it over a 3 yr period (I bought it in 2011, previous owner got scared to ride at 600 miles and rode very little after that time). Idle was all mesed up, I ran about four tanks of gas with Sea Foam (got better as it went along and I kep adjusting the idle spped). Finally all settled at normal idle for that MC (1200 rpm) and no more problems.
It is carburated MC vs FI and idle jets on it are a problem (must be kept clean).
I now have 43000 miles on it. Run a little Sea Faom in it now and then.