> It never occurred to me that the little grid signal voltage could have that effect
That's the magic of tubes. A great big bottle able to flow a lot of current, but can be controlled with a teeny grid signal.
With NO steady DC connection to grid, you are not TELLing the tube what steady current to flow. The tube has no real opinion on this, just sorta wanders. Could be zero. (Which would un-sag the PS to a high voltage.) What's this, a 6V6? Could be over 160mA. (PS sags to way-lower.) With a coupling cap from a previous stage, there's a strong tendency for turn-on and leakage to bring the big tube to maximum current. Which in an SE Class A stage is at least twice the designed steady current, and liable to smoke something.
> The cathode voltage, nominal 21v, goes up to over 50V.
We actually want the GRID-to-Cathode voltage. With a 100K-1Meg grid-to-ground resistor, grid "IS" ground (within a volt). WithOUT a grid to ground resistor, grid can go anywhere. In this case it wandered up to +30V or +50V. The cathode does not know the grid has got loose, so it obligingly rises to over 50V. 50V/470 is 100mA cathode current..... something's gotta give sometime.
Is a good idea to check all your grid-to-ground resistances, or at least the Power Tube grids, before turn-on. Maybe I will try that someday.