I think the best answer to career questions is to think outside of academic divisions. This is about you, not "a mathematician".
Start with the S&P 500 and Inc 5000 (in the U.S.—substituteI know you're in NZX 50New Zealand for New Zealand or FTSE for UK—although in my experience information on the internet is significantly U.S.-biased and as this is a learning exercisebut international research isn't a bad thing).
Learn what companies actually do and what kind of people they want to do those things. You don't need to honour the sunk costs of a Ph.D.