Skeet,
First off, since it is an 86, it should be strong enough for just about anything you want to play with in the 38-55 to 38-56 catagory.
If you want to have a new barrel and change chamberings I would suggest Wind River Rifle Company. They specalize in Winchester restorations and conversions. They also moved from SD to Ft. Walton Beach FL about 7 miles from me.
http://www.windriverrifle.com/home.html
I would suggest that you look at the Accurate Arms manual. In the rear they have/had a section on obsoleate BP cartridges, loaded with light loads of smokeless. Accurate 5744 has long been a favorite in cast bullet circles. You can get high density loads at low pressures with 5744. The old Lyman manuals have the 38-56 as does the Sharpe book.
There is one 38-56 load here along with a drawing of the cartridge and specs:
http://www.reloadersnest.com/frontpage.asp?CaliberID=81
You will note that the 38-56 was loaded by Winchester until 1936 and is a BP/Smokeless cartridge, like the 30-30 or the 38-55.
Best of luck,
Ed