Here's one of my cheats.
I need the headstock plate and control cavity cover to be under 1/8" thick but the board I cut them from is 1/2" thick.
My planer will go down to 1/4".
So, I glue my parts pieces onto a larger 1/2" thick board and run the whole assembly through and I can take em down as thin as I want.
The down side is that your pieces are running through the planer the same way on the same face on every pass so the planer snipe gets amplified after a while, which then requires much sanding to level out.
So, I prep the side I want to be the outside face first, then glue the pieces down with the back side up. That way, any planer marks I can't completely get out will be out of sight.
Gotta take care to use but a few tiny drops of glue, also, or the boards will never come apart again.
Don't ask me how I learned how much glue is too much glue...