empirevr:
The 20-bore/.577 is an altogether different cartridge from the .577 straight (either 2 3/4 or 3 inch). The 20/.577 is the 20-bore 2 3/4 inch brass rifle (or bore-gun) case necked down to .585. It is hence a bottle-neck cartridge.

If the chamber-cast from your 25-bore barrel mikes out as a .577 x 3-inch, then simply assemble components and load away. There is plenty of data for loading that cartridge, either with black powder or a 'nitro-for-black' equivalent. Do some homework on fillers though, if choosing to load the latter. A search should turn up a number of threads on this forum containing plenty of 'good oil'.

With modern N-for-B loads, you should be able to load to 7 or 8 tons pressure, much kinder on the gun than the original 10 or 11 ton loads with BP. The lack of corrosion with nitro is another bonus when trying to extend the lives of these marvellous old things.

BTW, many Brit and Continental 12-bore shotguns were bored 13-bore. As long as the chamber accepts the 12-bore case, no worries. Finding a modern low-pressure shot-shell to match the BP pressures (around 6,000 psi?) is a bit harder of course, though not impossible. I would recommend sticking to BP initially, in 2 1/2 inch cases rather than 2 3/4 I presume.

...and further:

...a few modern versions have been built in Melbourne, Australia, on the Greener 'Empire' action. An early thread by NitroX showed photos as I recall. It's a very practical combination for a cape gun IMHO, like the Paradox ads of the day "Anything from snipe to tiger!"