I sacrified three of those BSPQ and practiced on a scrap piece. The first one I pulled by the hand riveter, the others by the pneumatic puller at 40..45psi. All stems broke proud.
To install the doubler I followed Kevin's suggestions. I started with the 5/32" from outboard to inboard.
After each rivet, I filed down the stem. All stem broke proud 3/64" above the dome head. The trick is go slow and
to take your time while filing. Constantly check that you don't scratch the doubler or (even worse) the skin. There's not much clearance.
Then I installed the cherry followed by the AD41H and finally the LP4-3. (whouu 4 different types of rivets for a doubler plate

)
At the end, I smoothed the BSPQ row by 400 sanding paper and finally scuffed the doubler plate by scotch brite pad.
I am happy how it came out, but have to admit that it's much easier doing that during the build.
And yes, I did prime the bottom side of the doubler plate prior installation.