You're in a tricky balance situation. Everything is relative; so your "just a bit" can vary widely from another's "just a bit".
I'd suggest taking a damp 4000 grit pad and hazing the surface lightly, as a first attempt. I mean just barely remove most of the shine.
If that doesn't work, then try a 750 grit sanding plus a light polish.
(Be careful: you mention 800 grit, but most "800 grit" pads use the CAMI grading system [Scotch-Brite uses CAMI], whereas most abrasive pads, Abralon, Siaair, NEAT and Jost, use the FEPA grading system. 800 grit CAMI is roughly equivalent to 1500/1600 grit FEPA. So, if you use the light grey Scotch-Brite pad, which is 800 grit CAMI, the result will barely be any different from your 2000 grit current base grit level.)