need membrane sw w/encoder

What you have envisioned is probably not a standard stock item. The most straightforward approach would be four 1/4" SPST toggle switches. Each controls one relay with, if required, one set of contacts for the load and one for an indicator lamp.

Digikey carries a 4-position membrane switch

but you'd need to add the glue electronics.

I did. I'm sure any of these companies would be happy to provide you with exactly what you're looking for. Some NRE cost or minimum order quantity may be expected.

Well, if I were doing this I'd probably grab a small microcontroller with an internal RC oscillator for the clock, unless driven to another solution by other requirements. The uC gives me for "free" a power-on reset for the relays, software debouncing of the inputs, and I/O for the switches, relays, and indicators. If you don't have a drawer full of assorted micros within reach then something like a Parallax Basic Stamp or an Arduino may do the trick.

For a non-processor-based circuit, a D-type flip flop with Q* fed back into D and the switches to the clock inputs would do it. An RC circuit could handle the power on reset and another would do for debouncing.

The relay drive could be handled by a transistor switch (unspecified, since the relays, power, and loads are unspecified), with appropriate snubbers for the coil and load.

And the whole works would need one or more power supplies.

It's very unlikely that exactly what you're looking for is available for retail sale. Maybe the cat enthusiast forums? Or, you could get lucky and find one, or similar, as surplus/overstock at the surplus outlets.

WRT kits, I haven't dug deeply into their catalogs recently, but some places that may have something that could be adapted to your needs:

Good luck!