Edwin Jagger soap pucks look like they would fit nicely to that scuttle. I would classify them as average compared to such things as Tabac, MWF or Mike's, but by no means bad.
Have you looked into a glycerine based soap which you could melt into your scuttle to fit ? Cover the drain holes with some duct/electrician tape on the underside if doing this, then remove the tape when done.
Or alternatively, with tallow based soaps, grating a puck or stick into the available space and mashing it to a fit ? That should work too - or trim a puck with a knife (you can grate the odds and ends into it as you use up the trimmed puck, and again mash them in)