Happy to report that through the kindness of a gentleman in England that I contacted via the British Militaria forum, I now have a good set of barrel contour dimensions for a 45 cal Model 1881. The pattern rifle is a .450 No. 2 Musket.

The consensus here is that my rifle was probably originally a .500/450 No. 1 Express.
I am seriously considering going with this round, in the interest in keeping things correct.
Brass is available from Bertram, Dies from CH4D, and a reamer can be had from PTG.

But, the only dimensional drawing I have seem for this round is in my copy of Winfer's Westley Richards book. This shows the neck diameter of the No.1 Exp as .490". That seems awfully large. Most brass for 45 cal.(.458 bullets) seems to be .478 to .484.

Did the No.1 Exp brass just have an unusually thick neck? Or is it meant for a larger bore/bullet/obsolete rifling.

Before I commit to going to No.1 Exp. I will have to contact CH4D and PTG and make sure the standard reamer and dies are compatible with each other and that they will work with a standard .458 groove barrel.

The extra cost in brass, dies and reamer to use the No. 1 Exp verses what I could get the same for in .450 BPE is already several hundred dollars. But if I would have to go to a custom barrel bore and get into casting and sizing bullets to make things work, I will likely go with a more easily obtainable caliber.

Thanks to all for the great input.