Check out the Wood River (version 3) longer models, which are a great value and very well made. Not quite as elegant as the Veritas, but more affordable. Flattening, sharpening and very fine adjustment as well as technique are involved, but yes you can plane a board that size and get it very flat. Lots of videos on that topic. You will work up a sweat, but the sound of a plane making paper thin curls is very satisfying.
There are also people here who would suggest cutting the piece into smaller pieces, flattening and planing those, then gluing up panels for final use. Less likely to warp than a solid piece. Wood with a twist wants to keep twisting even after assembly. Personally, I would rather have a glued up section, which properly done, will make for a great final result.
The more I do, the less I accomplish.