How to build a linear LED driver that is dimmable?

It sounds like continuously adjusting the gate voltage of a MOSFET would get you what you want. I’ve done this a couple times using a voltage divider and an adjustable resistor, and it works well. It is very simple to DIY as far as circuitry.

If you want a more traditional clicky switch the LD-3 driver from led4power is a linear driver with no-PWM modes.

Or there are triple channel drivers like the texas avenger. You could put a different number of 7135 chips on each channel. This would only actually give you 3 pure linear without PWM modes, though.