You want to use the highest swingweight you are comfortable with. Trying to hit high bouncing shots the backhand with 300-310 SW is just going to make that shot even more difficult as you won't have the plow through to drive back those heavy balls.
If you are having trouble getting the racket around in time on the backhand I suggest increasing static weight and making your racket more headlight. Swingweight will increase slighty but the headlight balance will around you to get it around better. I keep my racket 13.3oz and 10pts HL; the backhand is my better wing and I can drive balls that are over my head because I let the racket and its heft do the work.
for me i have found a 299sw donnay yellow/silver light 99 squin strung at a low, bouncy 50lbs tension does well-er than other rackets i have used to counter the high-bouncy to the backhand...a firm flat pop sends it back deep and low, if not all that fast. it has bought me time to recover.