Yep...I've a few suggestions!
New battery, first thing.
Push in on the door a bit to take any tension off the bolts, work the handle back and forth a bit, just to make reasonably sure it's free/not binding.
Enter the combination and ease the handle to the open position.
Keep trying various iterations of this, perhaps with some jarring, extra pushing on the door, cocking the handle while operating, etc.
My safe had a quirk where I needed to rotate the handle slightly in the latch direction when I enter the combination, then rotate it in the open direction afterwards.
I wouldn't advise getting excessively rough in your operations. This slippage you described sounds like you need finesse and letting your frustrations get the better of you may make things worse.
If you can't get it open, call a professional. I don't know what that might cost, but I'm gonna go out on a limb and say it's less than you cutting the safe open and having to repair/replace it.