You don't have to lower the plugs much, some 1/5 of a millimetre should suffice. If you don't want to build a tool, a narrow strip over your finger should do the trick. I'd start with 180 and go to 400 before filling, then go from 240 to 400 before painting. Depending on how bad brush streaks you get, sanding from 240 or 400 up to 2000 before the clear coat and after that the same. When sanding a finish, make a 45 degrees turn at every higher grit and sand until the previous scratches vanish! Another rule for sanding is to never force the paper as that would only create balls of loosened grit and lacquer dust which will dig deep grooves. You simply can't make the paper cut deeper than the grit's height which is measured in micrometres.
And yes, after you've got finish over the bare wood you can use wet paper and another yes, sand the old finish over the edges. If your hand slips simply sand that area with finer grits turning 45 deg every time you change to a finer grit. The goal is to get an almost shiny matte surface - 6000 grit isn't glossy yet but compared to the scratches you have there it will look like perfect! The final touch can be done with a rubbing compound. Basically you can to use a regular coarse paste like Biltema Rubbing 36-629 already after 2000 grit wet and a swirl remover like Biltema Polish Premium 36-84 after that. Use the pastes all over the top to make the gloss uniform.