You may try Jim at Delta Gun Shop. He can reline and possible recut the rifling. I'd reline at last resort and 0.366" (9.3mm) liners are available. I relined a H&H rook rifle a few years ago as it was bored out to .410. I returned it back to .360 No.5 - are you sure this 380 is not a .360 No. 5? many times this designation is interchangeable, but really the same.
A 38 long colt is about 1/16" longer than a 360 No.5 (or 380), other than that identical.
Paper Patch a .358 Lyman bullet (2 wraps = 0.366") over 13gr. of 2F BP or 3-4gr Unique for a smokeless load.
Keep us posted.