Sounds to me like it would work. Would consider using 148 gr wadcutter as to have lots of bullet shank and use any 38 Special target load from reloading manual at about 750 fps. Might consider trying a hollow base wadcutter as is, it might bump up enough to seal bore.

Sounds like you have a 38 long (Ballard caliber) or extra long.  The long case is the same as 38 long Colt and the 357 Maximum case is almost identical to the XL case.  My remington measures .364-.3645 land to groove when slugged as it has 5 grooves so cannot get a groove to groove mic with an odd no. of grooves.  I found a 38XL mold on ebay a few years ago which is a heel bullet but a hollow-base inside lubricated bullet worked better.  A chamber cast would tell.  - James

Yep, the rounded corners got me.  Couldnt stay on them reliably with near equal width lands and grooves.
J.

I'm assuming that you are loading with black powder.  If not then ignore my suggestions.

Does the chamber have any freebore?  If not I'd try a bullet 0.006" under bore ( not groove ) patched with 8 lb Seth Cole paper.   

If it has freebore, then I'd use the same bullet but breech seated.  That works very well in one of my .38-55's.

Chris.

The chamber measures 1.185, so it's .035 longer than the .38 special case. Is breech seating a possibility, then?

I agree with coljimmy - it looks like you have a CF conversion from a 38 Long RF. The good news is that now you can custom fit your cartridge and bullet, which would be heeled for authenticity and provide you with the pleasures and disadvantages of that period of cartridge development. Several mould makers have appropriate moulds, often oversize for the purpose of working in any manufacturer's gun, as different makers had differing ideas about proper bore size for the old RF cartridges (and chamber size, chamber length, etc. - no SAAMI in those days). My 38 Long RF Forehand & Wadsworth works well with BP and a .375 Old West mould heeled soft lead bullet. Be very conservative if you try smokeless and keep the pressures within the BP range to keep your rifle from developing a larger number of parts and your body from having extra orifices. That said, measuring the chamber length and diameter, seating the bullet you choose (after checking twist) to get the right over-all cartridge length, and working up your load should give you a pretty accurate combination if the barrel is in decent shape. Ought to be fun, too.

Perhaps, but COW isn't a 100% reliable source.  Most of the time it's on the mark but every once in a while it drops the ball.  Close visual inspection is in order.  Consider a borescope?