I’m under the impression that No. 44 rim fire parts show up on E-bay pretty often.  Of course, then there’s the extractor and block pin variations, etc., to contend with.

What I’d do is paint a precision coat of spotting blue on the back of a fired .22 case and carefully insert it into the chamber.  Then I’d close the breechblock and so transfer the rim circumference to the block.

Comparison of this circle to the diameter of your firing pin will determine whether you can get away with an offset striking nose on your centerfire pin or whether you would have to enlarge the firing pin hole and offset a larger pin.

Then I would drill out the firing pin channel through the face of the block, make the offset pin to fit, make a bushing for the face of the block with an offset hole, and fit the thing together.  As long as I had to do this anyway, I would make the offset at 12:00 rather than 6:00 so it has a solid surface to crush the rim against, rather than the extractor on the bottom.

On one of my 44s, somebody filed a dovetail across the breechface and installed a flat strip of steel for the bushing.  It’s a much neater job in the small space available than threading a hole, driving in a screw, cutting off, redrilling, etc.

Let us know how it goes.  You’ll be the expert when this job is done!

Post some pictures of the particulars of your action on here or email them to me; I have a fair number of 44 part actions and parts, I'll trade you if I have something that looks like it will fit and if the condition is similar for your parts.  It will probably take me a week or so to find the parts and get back to you.