You can often find "orphan" amplifier switch pedals sitting in a plastic bin in music stores for a reasonable price. Some are pleasingly well-suited to use for what you describe, especially the ones made from extruded aluminum, with the switches mounted close enough to the front. I picked up a 3-stomp switch some 20 years back, and recently found it ideal for building myself a 3-effect unit, that I packed a compressor, overdrive, and Rebote 2 delay into.
Also, in view of your intention to build in 2 "distortions", you may be able to get by with a 3-stompswitch unit, and simply use a toggle switch to select between distortion A and B.
Perhaps your bigger challenge will be keeping the various high-gain signals from leaking into each other and causing unwanted oscillations. Either plan out a fabulously bulletproof layout, or score yourself some thinner-gauge shielded cable.