So, I finally swapped out the inner spring tonight. It was more involved than I had hoped.
The retaining washer was on pretty tight. I had to use a brass punch with some solid strikes. I did make sure it was in the recessed portion of the recoil guide rod. Since I only have two hands, I had to made a simple fixture with a few blocks of wood, a few washers, and a vice to keep the assembly compressed while I held the punch and hammer.
I also had to use the punch and fixture to re-assemble the washer. I think that next time, I will be spending the extra few bucks to buy the complete assembly.