Specifically, looking for the appropriate type of electrical or mechanical pump, which would suck gunge out of a bucket and pump it through a hose/tube?

Does anyone have any suggestions - presumably some of the producers with fancier setups have suggestions? I basically want to be able to have a bucket load of gunge pumped through a hose, directly into someone's pants!

yup. pond pump, the type for water features/ fountains, plus hose that matches the diameter of the outlet and a jubilee clip. protip - use a deep container as the pump needs to stay covered. also reinforced hose so it doesn't kink

have fun!

For low-tech home use, I've wondered whether a dinghy bailing pump would work, one of these guys (this one's a Whale Easy Bailer);

Do you have the gunge being pumped back into the container for a continual loop?

nope, I'd need a deep pit in the floor under my gunge tank for that to work instead of my 'not -quite-deep-enough-for-a-pump gunge collection tray. Sadly not to be, manually baling back into the container isn't so bad though

There are fluid pumps available powered by the common cordless or mains drill. Water flow rate is 40-50 litres per minute, a thicker substance would obviously be slower but even half a litre a second would likely get the result you're after.

Shop around and you'll find them for less than $20.

No motor or electronics to burn out, pump water through it to clean.

Speaking from personal experience, most smaller pumps are not up to the job of pumping gunge. We've had several submersible pumps over the years to empty the dunk tank and the only way to get them working was to dilute the gunge down. Even with a petrol Diaphragm pump we struggled where there was lumps in the gunge.

A sump pump specifically designed for effluent and solids as large as 2" are available.

Thanks all for the suggestions ... I will get investigating!

I feel like if you've invested this much into it, you should just create an additional basin in your basement, and install a separate gunge sump pump.

Not possible - no basement under the studio, plus studio is finished now and I'm not jackhammering out the expensive non slip floor and taking a further 6 months and jeebus knows what cost to get going just to save ten minutes work here and there

I like that I can do longer gungings with it, and that's enough for me

sump pump sounds interesting, but my pond pump system is working gorgeously. Just takes a bit of experimentation with flow rates. I will look into sumps though...

A little warning about pond pumps. I have a few of the big ones (got them cheap at Harbor Freight) and have been testing them for use in a water feature I'm building in the back yard. The ones with a 1.5" or 2" outlet will send a jet of water the size of your arm about 20 feet in the air. Be careful.

Have you tried a fire extinguisher?