Let me weigh in here.

Saying you have nice Martini action to build on is like saying you have a nice Winchester Lever action to build on.

Which Martini Action do you have?

Most common coming up in this discussion is a Greener shot gun action. Greener does not recommend building centerfire rifles on the shot gun action.

That being said I will confess to building number of centerfire guns on the shotgun action in the past. All my guns were built on the solid actions. There is a version with a split receiver. The bottom of the action is split right I front of the trigger guard. I believe this split is to facilitate take down.

I am also aware of a number of 45/70 being built on the Greener Shotgun action. These are probably okay as the chamber wall will be pretty thick. In a split action chambered in .577 I would be concerned about the thickness chamber walls over a split.

Some Martini actions may be able to be adjusted enough to accept a 577- 3" case. In the Greener shot gun the case is longer than the breech block. (At least on the two I have here). Loading an empty case into the breech results in the rim catching on the back of the knuckle and and mouth of the case is stopped by the back of the barrel.

The 2-3/4" case is accepted with the a deep seated bullet. I have a dummy case made up with a 650 gr. bullet.

There are other size Martini's that might work.
here are the ones I checked.

1. Sporting Martini on MK IV action short lever
2. Hollis Action-definitely
3. Westley Richards ZAR
4. Greener Sporting rifle action.
5. British Military MH action

Two other possibles. Both of the these guns are in .303 and the chambers were not big enough to gauge the .577.

1. Greener sporting rifle on Tranter pattern action
2. Holloway and Naughton sporting rifle on Bonehill sporting action.

These all most likely with take a 2-3/4 NE.

You may be able find a chopped up ZAR, they do show up once in a while. But a complete rifle is to valuable for this project.

British military Martini Henry. The volunteer patterns often only have maker name and can had fairly inexpensively. Especially the Afghan bring backs. There are some Mk II's that have faint markings. I have an action of one of these here right now.

I also checked these actions with an empty 3 inch case. This is doubtful. Maybe. The load position may be adjusted to work. Ask your gunsmith how he is going to do it, if he says he can. If he says would grind the loading trough in the top of the block out a bit, grab your gun and run. The breech block is the equivalent the locking lugs. You don't want to do anything to weaken it-like grinding the trough.

I have dies for CH4D. Moulds from CBE. The big issue I have is getting the 3 inch brass trimmed to 2-3/4".

The Greener shotgun action is difficult to assemble and reassemble and thus difficult to work with. I had a lever device at one time to work the block, but some time over the years it has walked. Most likely made into another project.

Couple that with brass trimming issue, my gun sits in the safe gathering dust. I need to finish the stock.

I do have a chambering reamer for the 2-3/4" version.