Paul,
You know my opinion on the barrel and I do agree that finding the the factory breach will be difficult. I have a 1950 F-1 Ford truck with a 51 hood and front fenders. The problem I have with finding the proper front clip in decent shape is that it is always attached to a equally good truck.
This may be old hat to you if so, forgive me.
I stated earlier that a True Hawken was difficult to build. That is true. A late Hawken half stock can be a night mare of wood to metal fit.
Now a Plains Rifle like a haflstock Leman will build like a longrifle with the exception of the underib. A Leman Plains rifle might be a good candidate for that Browning bbl. You could build it in a short full stock or half stock. Full stock is less work.
Heres some facts about modern " Hawkens" The TC, Invest Arms, Cabelas, CVA, Traditions, and even the venerable Great Plains Rifle by Lyman are not Hawkens at all. The TC and its clones are patterned after mid western half stock rifles of the 1870s. The GPR looks like a light Hawken Rifle but it is constructed more like a long rifle.
Probably the most difficult thing to fit on a true Hawken halfstock is the trigger and trigger gaurd. The trigger guard threads into the trigger plate. That makes the whole trigger group a one piece assembly that can be very difficult to fit. If fit separately they may not fit right when assembled.
A long rifle or simple plains rifle on the other hand, the triggers can be simply pinned into the wood or inletted in place. The trigger guard is a separate unit that can be bent to the correct shape and placed over the triggers. A much simpler method. That's how the GPR is built if it were built like a true Hawken it would cost 12 to $1500.00
You can build a rifle that looks like a Hawken but is not really built like a Hawken. Many Hawken style components are available but they assemble in the simpler manner.
Here is some eye candy for you. The first is the Nez Pearce Chief Joseph's Leman
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http://www.wrtcleather.com/1-ckd/firearms-trade/chief-joseph-leman.jpg)
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http://www.wrtcleather.com/1-ckd/firearms-trade/ndn-guns-002-leman.jpg)
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http://www.wrtcleather.com/1-ckd/firearms-trade/leman-trio.jpg)