I really dig the LaFrance M14K.  Are there any gunsmiths out there that would build one?  Years ago Ron Smith said he was going to do a run, but it never came to fruition.

How short is the barrel?

If you are serious about this project you should contact John Thomas at Retro Arms Works. He can be found in the retro forum and his work is museum quality. He built himself a La France M16K a couple years back and is a master machinist. I had him machine/alter a bm59 tri compensator to slip over and functionally screw onto a AR bbl on a retro prototype carbine build I put together. He is a full service shop with excellent communication and great shop rates.

Have a look at this.....http://shuffsparkerizing.com/services/the-mini-g/
Maybe he can help you as well.

How short is the barrel?

It's 13.5", but the muzzle device can be pinned.

John Thomas at Retro Arms Works

Good lead!  I am going to check him out.

Shuffs

Another good lead!

Thank you gents.

Not an NFA-type (sub-16" barrel) , but perhaps something close ...

You can get this built as a 16.1"  "BM-59 carbine," which accepts M1A mags:

http://shuffsparkerizing.com/shuffs-bm14-garand/

I have what is essentially Shuff's mag-fed Mini-G variant. It's a standard Mini-G converted to run off M14/M1A mags. It has his custom bolt stop (as shown on the page linked above),  and runs a Schuster Mfg M1 muzzle brake.

You can also add a forward rail for mounting a RDS, scout scope, or whatever.

Weighed side-by-side against my buddy's 16" S.A. SOCOM, both running a sling and an empty 20-rd mag inserted, my mag-fed Mini is lighter.

Here's the YouTube vid on Shuff's M1 ---> BM-59 mag-fed conversion.

https://m.youtube.com/watch?v=SkjTOHFbQLg&ebc=ANyPxKqoTy1VG-_fLl64E2CjVhKdhw23-oPr7AMZtf2wXPKJQtoJjGaq-Tl6Gp6SCAtqgfr4p2dlBxtXfAm7BbmdH5riV_lasQ&time_continue=4

Looks promising.  I will consider this as a back up, if I can't get an answer on the others.