Some scope/mount/rifle combo's just don't work together. A little more info would help, I'm assuming that is a Burris FF-II and the rifle looks like a short action, but I'm guessing. Burris scopes have adequate eye relief for most people. And it already looks like it is mounted too far to the rear, it would be for me.
I can't be of much help with a different scope, the one you have is my go-to recommendation for anything under $500. As a rule Leupold scopes have a bit more eye relief than most, but Burris isn't far behind. You'll need to stay with a full size scope. Look at specs, lots of modern scopes are shorter than older scopes and won't fit long action rifles. You rarely have problems with short action rifles.
Scopes with electronics are a lot heavier and I'm not sold on their usefulness on a hunting rifle. I had one on an AR for a while and I found that if it were so dark that I needed the dot on it was too dark to see the target. I never turned the light on other than to play with it initially. In most places legal hunting hours are from 1/2 hour before sunrise until 1/2 hour after sunset. There is adequate light with a quality scope during those times. I know of at least one state where it is 1 full hour instead of 1/2 hour.
FYI, you can install those mounts in either direction in order to make them fit some scopes. I'd reverse the rear base if it were my rifle to center the adjustment turrets between the rings, but it is the rear base that is limiting your adjustment in this case so that wouldn't help.