Tino:
My preference would be for a fully-rifled 12-bore, and shoot big conicals at modest velocity! ....but then, I'm a little strange that way!

Most of the big NE cartridges are relatively low pressure, but still much higher than a shotshell. Nevertheless, I could recommend the .577 x 2 3/4 Light Nitro, as I know it will fit (just) through the MH action. Most of the long NEs won't go 'around the corner' and into the chamber.

The .577/.450 Martini Henry cartridge was designed to go 'round the corner', and did have an express loading for big game a century ago. Today it could be loaded with a light nitro charge and jacketed .458 bullets to make a potent hunting cartridge. Brass is available. If using an original barrel, check the groove diameter though as it might not be .458.

Do you already have the police gun? If not, you might be better off with a standard Martini Henry or Martini Enfield rather than the shotgun variation, because those actions have more metal behind the hinge-pin than the GP or police-gun.