Some progress, I gave the balanced valve a go and was able to raise firing pressure to 1100 psi.

Video of some initial testing with this setup

Best velocity recorded was 774 fps for 59.3 ft lbs, around 50% more than the maximum for the conventional valve.

I was a little conservative with the diameter of the balanced portion, I was worried that if it was too close to the seat then it might have problems sealing.

In that regard I've probably erred too much on the side of caution with 7mm, and can afford to go a little higher...

More to follow, I will post more details of the valve once I've optimized it further.