Phil,
First of all, I'd say "Don't do it".
I considered doing it with my Hollis. Decided that the reregulation that might need to be done wasn't worth the effort. If you are going to "restore" the rifle, then as stated above you need to do the whole rifle, reblack barrels, refinish the stock. . . ..
I decided that I'd rather have a working double than show piece.

Having said all that. . . .
Since there is no A. Hollis and Sons to restore the rifle, here is what I would do. The only people I would let case color my rifle would be DOUG TURNBULL
They know what they are doing and they do bone charcoal case coloring. They have a good reputation .

The only person who ever does work on my rifle is JJ Parodeau at CHAMPLIN FIREARMS Enid Oklahoma. JJ does outstanding work. He doesn't have a line of BS, just solutions!
JJ is a Master Gunmaker! I have seen him replace the barrels (resleeve) on a double. He does stock work.
He reregulated 400 NitroExpress's Hollis to a 60 cord rifle. JJ is trusted by several members of this forum.

I'm sure that there isn't a shortage of good double rifle restorers in the UK. I have seen several rifles that have been restored by Westley Richards.

Phil, in short, you can restore it. It's just time and money and finding the right people to do it.