Trap Bar Narrow Grip Issue

I recently switched to a Trap Bar for DLs (Bells of Steel Trap Bar 2.0). Not using the "upper" handles, but the ones parallel with the bar (same height as if I was using a straight bar). The Handles are significantly more narrow than a barbell and create more grip/hand issues than anything else.

Is there a some way I can thicken the handles to match the diameter of a normal barbell? Or am I just gripping it wrong in the first place (suggestions)

I am only doing sets around 375-400, and don't feel like i should be adding straps at this point.