It sounds like the folks at RS are using a different staple than in years past. About 3 years ago I completely replaced all of the whiskers on a 54 and they had the correct staples at that time. The trick to getting them deep enough into the whisker so that they don't scratch the glass is to spread the nap a bit with your fingers and then insert the staple. Having been a carpet installer for several years and working with close nap Wilton wool carpet, I borrowed that trick and it worked.
And, you will need to reuse as many of the clips for the inner upper door garnish molding as you can. RS didn't have any at that time and as dumb luck, I had a jar of NOS to fall back on.
The job is not easy, but can be tackled by anyone with patience.