would you have to reverse a nut to put it on the thread?

Yes – a thread is cut in the same direction as it works!

So looking on the end of the screw, a right-hand (conventional) nut will turn clockwise to put it on, a left-hand, anticlockwise. The die runs in the same direction as the nut will.

NB: if using a left-hand die on a lathe with a screwed-on chuck, there is some risk of the chuck unscrewing as the die bites into the metal. This less with a small thread like M6 but it is still best not to try it under power.

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While here it is worth re-iterating what a post on here some while ago raised:

If you are threading raw bar-stock, not a diameter you have turned to suit, measure the bar before trying to thread it. Depending on the metal and supplier, it can be sufficiently above nominal diameter, and even out-of-round, to make using a die very problematical.

Skim the intended length of thread to a few "thou" or about 0.1mm below diameter, or if possible to the standard outside diameter given by the thread-crest rounding. (You will find such details in reference-books or charts.)

Ouch, that sounds like a real oddball. For an external thread the obvious answer is to single point it.

M6 X 0.75mm is standard ISO Metric Fine.

Possibly unusual, and in left-hand form unusual-er still, but I'd try Tracy Tools first, or the Tap & Die company.

Scrub that, forgot lh.

There seems to be a number of Chinese suppliers via eBay, but also one German one if you search for EU, rather than UK
Those are made by Baer, which led me to look at their own website HERE
https://baer.tools/en/taps-dies/thread-standards/mf-metric-fine-thread/round-dies/for-left-hand-thread/3514/baer-cutting-die-mf-6-x-0-75-left-hss?c=860

Bill