Best way to flatten records is an SME style of system. Screw on clamp
with a specially shipped bottom and a washer under the record.
25 or so years ago I had an Ariston TT, the "minimalist" round one (RD40?) which used that method. Very effective. Since then, I've made very simple mods to a clamp that accomplished the same thing: total flatness. It must be a clamp, not a weight, as it needs a positive grip on the spindle to hold it down.