Most people avoid using steel wool as the fibres they leave behind do tend to get everywhere. It has its place, but I'd avoid using it if I had alternatives.

I'd be wet sanding to get rid of those lines, using various sized blocks to keep the paper flat as possible. I might start at P600 to get the worst of the lines off and get a generally smooth finish all over, then run up through the grits to maybe P1500. Or you could use wet MicroMesh pads or cloth. My MM cloths run from 1500 to 12000 and 1500 MM is slightly finer than P600 paper, so you could run up the MM grits up to around MM 4000, which is equivalent to P1500.

But you are still likely to add some more lines with the final coat, which will need levelling with the grits again and then polishing/buffing, so you could do a rough P600 level now then just do all the hard work once the final coat is on and cured.

There is a difference between 'drying' and 'curing'. 'Drying' is the first phase where the solvents evaporate. Once they've done that, then the finish is in the second 'curing' stage where it hardens. Final curing/hardening can take months - one of those exponential asymptotic curves where it takes infinitely long (almost as long as a '70s prog bass solo) to reach the very hardest state it can. But there is a 'hard enough' state that's reached after a few weeks (it obviously differs from finish to finish) where it's almost, but not quite there; but will still polish up to a great shine.