If I had to have some work done on an Alexander Henry double I would suggest having Nick Makinson or Les Paul do the work. Both are English gunsmiths and they both live in Canada. I have had them both do work for me and the results were great. You can look both of them up on the internet. I have an Alexander Henry hammerless like yours that is .450 x 3 1/4"
BPE cased with full accessories. I can take pictures of the action of my rifle if you think that it will be helpful. When I had Nick Makinson do some restoration work for me he had a U.S. address that you can send the gun to which makes things much easier.