I had this problem when a city of mine hit 650k citizens. It spread like syphilis across my city and I ended up dropping roughly 150k citizens. My main problem was too many jobs were being outsourced to neighboring cities along with there not being enough to provide for the population all together.
Since your problem is primarily with R$$$ its probably jobs specific to that wealth level are either not close enough or there are just not enough of them in general. Those being High Tech Industry and Commercial Offices. Check your R$$$ populations against those types of jobs and see how it matches up. If it doesn't match up, then expect to do some rezoning, or zoning for more development of them. If it does match up, then it is a transportation issue.
I just checked back and forth between my cities, paid more attention to those values and was able to fix my problem. It was time consuming, I did a lot of rezoning, but it ended up working for me.
Oh and since you are at the 250k mark... a problem I had when I hit that was even though my EQ level was high, the education grade on the query was low. If you have an Opera House placed... make sure you download the mod to fix it. Its treated as an educational building and they didn't give it a funding slider. After getting that fixed my pop jumped nearly 100k.
Personally, I've tried the whole building a neighboring city simply for industrial development. For me it only worked until my Residential and Commercial city reached a certain population and I was plagued by the brief case of death. Maybe my transportation networks were always shoddy, but I've always had the most success when I built my cities to sustain themselves by mixing all types of jobs and residential wealth levels instead of pushing out the dirty and poor on the neighbors.