In the SCA we fought with Rattan swords. The Rattan is round and thus we had to mark our 'edge' with tape. Still, its hard to keep a round weapon from striking true on the edge. The same goes for our PVC weapons. Weapons made with the more expensive firberglass rods are not so round, but round weapon core's create round weapon grips.
Round grips sometimes swivel in the hand, especially if you've been fighting for awhile and your hands are sweaty. Gloves may or may not alleviate the problem. How you cover your handgrip may help to. Some folks use super glue and string, other's use tape, and some use cusioned grip tape or just plain cloth tape. All can work, but sometimes even then it may swivel in the hand causing your strike to hit on the flat.
Though not period or historical, the use of a 'trigger' may help. A trigger is a strip of webbing or leather. You form a finger sized loop with it and attache it either to the front or side of your handgrip. With Rattan weapon cores you can use a screw to screw it in place. For us, we could use duct tape or electrical tape with a final coat of cloth tape.
The trigger is set so you can slide your index or middle finger or both, through the loop when you grip the weapon. In this way, your finger's keep the weapon from 'swiveling'. Adjust it so it fits the way you want it. Test it out and see if it helps with your control of the weapon.
I was having trouble lately keeping my handaxe blade on target so I put a 'trigger' on the front of the grip and want to try it out at practice to see if it helps. I made a finger sized loop of suede leather and taped it in place top and bottom.
For a long hafted weapon you could probably build a long trigger that encompasses all your fingers and keeps your hands held in place and tight to your weapon. You should put these down the front or 'blade' side of the weapon.
Konradr