Well first off, the wedge slot orientation looks good in both barrel and arbor. You can tap the end of the arbor for an adjustable wedge bearing (like I mentioned) so you can use the wedge you have. I think the slotted set screw is an old fix/repair attempt but my be factory (I think I've seen those before). In either case, that is no fix for a loose arbor. The arbor needs to be removed, material at the "shoulder" upset in 3 or 4 places and then torqued back in place. That's the correct way to correct a loose arbor. Since yours has a set screw, reuse it. Install the barrel assy before torquing the set screw . Almost all others use a pin which has to be drilled out. I use an 1/8" bit and an over size pin (not hardened). Same as above, reinstall barrel assy before installing the pin.
After the arbor fix, drop a washer in the arbor hole to check for a short arbor. The method pictured isn't a reliable test. The tension applied by the "driven in" wedge is rather significant and will close down the barrel and probably lock up the cylinder. I've had folks swear up and down "theirs isn't short" . . . only to find out the washer wont interfere with assembly.
Mike
