No guarantees, but I think the standard Martini action should be strong enough for the .577 'N-for-B' equivalent. I believe plenty were so-chambered in the late 1800s.

I have never been able to understand the infatuation with the GP Shotgun or Police-gun actions. The standard rifle actions should be much stronger, and are a lot more available (a hell of a lot more of them were made than the GP version). They are similar internal dimensions, but provide a great deal more 'meat' behind the action block than the shotgun variants, which were cut away behind the breech-block hinge-pin, presumably to reduce weight. This is hardly a consideration when rebarrelling to a 12-bore rifle or .577!!

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Rifle Action on the left, shotgun action on the right.

I reckon the rifle action looks more elegant than the hump-back GP shotgun anyway!