Hi Jasper and congrats on your lovely plot.
Mustard sown September may have time to flower before winter, but not set seed at all. I would leave them to die overwinter, and if there has not been enough frost by mid February say, cut them at base and compost all the tops, the roots will not regrow.
Phacelia is more persistent and you could do your option 1, and/or try cutting some too at ground level. I am unsure if phacelia may regrow, but it’s better for soil organisms if roots are left there to decompose.
