Somehow we're going about this all wrong.
The wedge won't go through. That means the slot in the arbor and the slot in the frame window are out of line. The wedge drives against the arbor slot, at the front, and when you drive it further, it cants back so much that it hits the frame window on the right side of the barrel, can't go into the other side of the window, to lock properly.
Driving the wedge, with a feeler guage, to get proper clearance, just means you have an improperly fitted arbor, too short. If you can tap the wedge and close up the barrel/cylinder gap, any, let alone enough to lock up the cylinder, you got a bad gun. (Man, how I hate to keep saying that, and how I hate that many of you think the barrel assembly should "float" on the arbor, you get to adjust your clearance.)
To the OP, if you have over about 1/16 of arbor showing in the front of the frame window, you CAN file or grind a little to allow the wedge to go all the way through, just try to stop when it JUST enters the other side of the barrel assembly. No sense filing so much you need a new wedge in 6 weeks. If you can't get it into the whole slot, try filing the wedge down, first, if you can get it to lock up, bye'm'bye, you will wear in enough that a new wedge should fit.
The wedge will ALWAYS cant back. You mate up with the arbor at that diameter, you mate with the 2 sides of the barrel assembly window on both sides, has to cant, slant, to the rear, single contact at the front, contact on both sides of the barrel assembly window at the rear.
Cheers,
George