Bill Tindall, E.Tn.
I have an 8" jointer. I don't intend to ever own anything wider. Hence, I was driven to learn to sufficiently flatten what the jointer can't by other means. I was surprised at how trivial a task it became. In my case I use a scrub plane. But if I did flatening every day it would be with a power hand plane, likely an inexpensive 4" power plane.
I don't know what you have for a thickness planer, but if it is deficient then the money would be better spent on a machine with a large bed like any of the old light industrial planers in the 18-24" range. These machines can run a 5 HP motor on single phase. With a large bed on a planer flattening only needs to occur on the diagonal corners of the bed foot print.
My last two chests of drawers involved 17" x 36" single board panels for the ends. I didn't spend over 5 minutes getting each flat enough to thickness plane. Flattening meant nipping off the high diagonal corners until the board didn't rock on the table saw top. Then it was off to the planer.