@odie I have wet sanded with both blo and poly, and mixtures of the 2. Not a DO fan, but the blo/poly mix approximates it. Both flat and turned work. Easier to do with flat work as the grain isnt changing as much.
Difficult to do by hand on turnings. I rotate the piece on the lathe at 100 rpm, slow as I can go. As you surmised correctly that getting rid of visible scratches that way is difficult. The grey scotchbrite is too coarse and the white doesnt do a lot.
I have the same issue - scratches after I start applying finish. I wasnt pleased with the process of wet sanding (I now use it to fill small defects if needed, like punky tear out) so I worked at changing the process - get better at surface prep to do away with the scratches.
I had been using the short stroke ros mini air sander from HF. It worked fine but I wasnt pleased with the finish - I could see “paths” of scratching even with 800 gr, and I didnt like the air consumption.
I was never willing to buy an expensive small electric ros. I found a relatively small random orbit polisher on amazon for ~$80. Came with a 3” backer. I got a thread adapter and mounted the 2” backer from the air ros, since all my discs etc are 2”. It has an 8mm orbit, bs about 1/2 that for the air ros. I’ve been pleased with the final surface it creates, I think the larger orbit actually helps.
With a drill I found I got some deeper scratches that were difficult to remove, and the orbit motion gives me a more consistent scratch pattern.
I now use the drill to get an even surface, ie any heavy sanding, whether I start with 120 or 220. Just depends, but I usually switch to the ros by 180gr, up through 800. Much closer inspection before applying finish. I’m creating and missing fewer and fewer scratches.