Insulate Floor with No Crawlspace Access
I'd have to go with #5 as the better way and only right way. If the partial new floor has to come up for radiant heating anyway, and it does, then I'd strip everything to the joists and do it right with screws. You'll be eternally quiet, solid and comfortable with the heating protected by the subfloor and reflected up by foil-faced insulation for maximum efficiency. Make it all pay you back.