I've never used the 'correct' LMR style connector. I also never used anything other than regular whatever I could find at the surplus houses connectors on 9913 (also foil and braid).
What I've ALWAYS done is strip back an extra 1/16th of an inch of foil covered insulation. Done.
I just built a bunch of cable assemblies using BNC and LMR240 doing the same thing. This was to GPSDO my entire test bench.
Having the correct stripper for the job is more important than the companies 'approved' connector.
Then again, I made up connectors for 75 ohm hardline back in the day, too. For PL259. And they didn't make any from the manufacturer.
--Shane
WP2ASS / ex KD6VXI