You are right.
The spring on the wedge will rise up if the wedge goes far enough through the barrel and appear to catch on the barrel.
Your use of the pen cap to hold it down was smart in that the pen cap is soft and won't mark the finish of the revolver.
But the wedge very likely would have come through the barrel for removal just by using the wooden piece.
Eventually the wedge will loosen to the point where it can be removed with thumb pressure only. Until then, you have to use a soft tool to get it out. The thing I use is a small piece of brass round stock that is filed in such a way that can be pushed into the wedge slot up to about an eighth inch. The best way to dscribe it is that it looks like a screwdriver with a very thick tip.
I support the pistol with the wedge side (left side or "port side" for us Navy guys) down. Hold the brass tool against the wedge, then lightly tap it with the smallest ball peen hammer I own.
Wedges on new revolvers can be very stubborn the first time they are removed. I own more than thirty cap and ball revolvers and only a few of them still require the use of anything but my thumb to remove the wedge.
Other members will shortly wade in with other ways to get the stubborn ones out.
And sooner or later someone will tell you how to tell when the wedge is at the proper depth in the slot.
You are going to love this stuff and this forum too.
My reading of history convinces me that most bad government results from too much government. Thomas Jefferson