I am surprised that folks aren’t mentioning Epiphones - many had narrow nut widths - I have seen 1 5/8”. And many can be hand for a reasonable price, although above $1100.

I mentioned Epiphones in two prior posts, as did at least one other member, so we're definitely on the same page; the problem here is that the OP is looking for an acoustic archtop and, except for a very narrow window during the New York era (mid/late '37 through 1939), Epiphone necks tended to be somewhat thicker than many of their contemporaries (although they can often feel slimmer than they really are - I've played a fair number of vintage examples and owned a '46 Blackstone). On the other hand, by the time Gibson ramped up Kalamazoo Epiphone production in the early '60s purely acoustic archtops were essentially an anachronism; while you'll see a (very) few examples from that era - many of which were produced in whole or part from leftover New York parts (particularly the flagship Emperor and DeLuxe models) - you're far more likely to find a Gibson L-50 or L-48 (both of which were cataloged through 1970), the latter examples of which would have had the 1-5/8" necks shared with the Gibson/Epiphone hollow/semi-hollow electrics...

Id look out for a 1930s Kalamazoo KG21 or 22. Slightly deeper mahogany back and sides.
Light and powerful, w more bass than a typical maple archtop.