The wedge doesn't need to come out all the way. Just far enough to let the arbor come out. That little screw is the capture screw that prevents the wedge falling on the ground.
In a proper fitted gun the nose of the arbor is supposed to seat firmly and lock against the front of the hole in the barrel assembly. And at that point when seated solidly the barrel to cylinder gap should be set to an optimum distance.
The wedge is supposed to bear on the front edge of the slot in the arbor and the rear edges of the slot in the barrel to force the nose of the arbor against the end of the hole.
That's how it's supposed to work. But all to often the arbor is too short, or the hole too deep. Pick one
When this is the case the wedge has nothing to lock against in a proper manner and it ends up being used to adjust the cylinder gap. And that's just plain wrong.
Mike at Goon's has written a lot on this and when he gets an open top this is almost certainly one of the first things he checks for.
I'm not doing this for a living but I'm a keen hobby gunsmith and I ran my own thread on this and how I fixed the four open tops I've got here. It involved making up a small spacer button and after fine tuning the fit soft soldering it to the end of the arbor. I also did a couple of 1871 open top Uberti cartridge guns for a cowboy action buddy using this same method.
Here's a link to the thread I ran a bit over a year ago on how I did this and a few bits I made up to make the job easier;
http://www.thehighroad.org/showthread.php?t=785288&highlight=open+top+arbor+button
Others have packed the end of the arbor with a ball bearing or a small washer or some other spacer to fill that spot. I did that for a while too but I kept forgetting that the fill was in there and I'd end up dumping it out and losing it.
When the arbor is fitted or packed correctly the wedge won't feel "springy". Instead it slides in and gets very tight all at once with very little movement apparent after the initial contact.
The arbors are often tight and I'm not always sure why. If you want clean up the arbor so it's bare metal and coat it with a felt marker. Slide the barrel on and seat it. Remove again and where the felt marker is rubbed away file off a thou or two of metal. Re-mark it and try again.
I would not go too far in this and produce a "drop on" fit. Instead just get to where it's a firm but not tough job to seat the barrel and call it a day.
If you have the tools for it and if the felt marker rub points suggest it check the arbor around the wedge slot for signs of being "kinked". If it is you can try to carefully bring it into a straight line if it seems like this will cure the tight fit. I check mine but so far have not found a kinked arbor so I can't offer more than the suggestion to "read" the felt marker rubbings with an eye which is open to all possibilities. Assume nothing and expect everything.