Is your Outback an XT model? If so, then you have the same power as the Ascent which is rated for much higher tow rating. Suspension is weaker which can be addressed after you try to tow that RV.. The CVT is fine, although I do recommend using manual mode and "shifting yourself" in manual mode so the belt isn't always changing ratios or unlocking the torque convertor. CVTs have a bad reputation from 2005, but I am not hearing of common recent failures of 2015+ models even from abuse.
I tow an open landscape trailer, 12x6.5 with about 2500 pounds loaded (and no brakes :) ) with my 3.6L and CVT. I would be comfortable towing that Little Guy teardrop with mine. I can monitor the trans temperature through my infotainment system, and I expect that is still available with the later 11" screen. If the temps get over say 240* F for short times or 210* F for 30min+, then a transmission shop can install a higher capacity cooler than stock.