I managed to get the holes drilled and was able to get the screws to thread in the screw plate. It wasn't easy to get all the screws in when I test fit the base, but with a little work, I was able to get it to work. Sooo, I put some sealant on the base to mount it on the deck and started screwing it down. I had all 6 screws started and was screwing them in, however, when I got to the last screw it stopped halfway down. I tried backing it out. No luck. I had the infamous stainless to stainless galling that I was trying to avoid. I had thought that they were sufficiently lubricated, but alas, no.
The screw eventually sheared off and I removed the rest of the screws and the base. I was able to drill the broken screw out, but now I was worried that the galling had damaged the metal more than re-tapping could fix. I went to the hardware store and found a stainless hex head cap screw with the hex just a bit larger than the screw I was installing. I enlarged the hole in the deck to allow me to drill and tap the screw plate below the deck to accept the larger cap head screw. I then drilled and tapped through the hex on the cap head for the original screw. I screwed the cap head screw in the plate and installed the seat base without any more problems. Just another of the many minor setbacks along the way.
I like how it turned out. I just wish that the base plate had 6 hex bolts for mounting instead of three. Not worried about it functionally, just aesthetically. Maybe I'll glue some dummy bolts on just to make it look finished.