A plate reverb consists of a steel plate attached to a frame, under tension. The sound travels along the surface from and to transducers placed on the plate. They're quite heavy: the EMT140 (an industry standard) weighs almost 600 lbs, most of which is the framework that keeps the tension on the plate.

So,
and I think you can tell from the Title where I'm going with this, if we make a sphere of the same material then pressurize it to give the proper tension, we have a device with, as far as I can imagine, superior qualities, for a very small fraction of both size and weight.

Math:

The plate in the EMT140 is 1m x 2m x 0.5mm.
The material it's made of (cold-rolled steel) weighs 7,850kg per cubic metre.

Therefore the actual plate weighs only 7.85kg/17.3lbs
2 square metres is the surface area of a sphere of .39m radius

Our Sphereverb will be about 2'7" in diameter and weigh less than 20 pounds.

(I haven't been able to dig up tension specs yet, so I have no data on the amount of compression, thus none on the possibility of using ovoid, ellipsoid, x-oid shapes which would give much more variety).

Simple geometry is the enemy of good-sounding
reverb.

I'ts important that the "tail" or decay of the reverb
be fairly uniform at all frequencies. It's unlikely that
a simple shape would show these characteristics.

//simple geometry// but if I said "x-oid" then I couldn't make the semi-pun sphe-reverb.

Easily solved by either manufacturing it with an irregularly shaped "cork(s)" of a different substance for the reflections to bounce off of, or to make it not-quite-a-sphere.

I can't help thinking there's a perfect mathematical shape which would result in a perfect wash.

A cylinder would be functionally the same, as far as reflections are concerned, as a plate, but there's gotta be something better.

Just to rereiterate, this idea is the opposite of the one that doesn't work (and got all the buns) :D

The sound travels across the surface of the tank, and the inside pressure keeps the surface taut and has no aural purpose.

Like [csea] says, a simple sphere is much less than optimal (sorta crappy in fact). However a round-ended enclosed cylinder (ie: two halves of a sphere and a tube) gives the same overall acoustic results as a real plate, and there's probably even better shapes.

I doubt it would be high pressure. I haven't found how much tension they put on plates but a modern grand piano has 20 tons. A plate reverb wouldn't come even close to that, but even if it's 10 tons on a 3x6' plate, that's only equivalent to an extra half atmosphere in a pressure-vessel with equal surface area.