Just my opinion; so take that as you want...
Tyvek house rap over the existing; vertical 1x4 "nailers" every 16" on the studs; then hardi plank and trim; nailing (or screwing), only at the nailer. I would use an aggressive, 2.5" ring shank nail for my nailer board, (2x4 might be better), so we are sure we have are nailer into the studs. My worry is nailing hardi directly to the existing siding; we want our hardi tied back to the structure, not the veneer.
The other route; blast the siding and a Good epoxy paint System on the existing siding. Not some home depot primer and exterior paint; i do mean a proper epoxy paint system. This isn't 1970 anymore; and the world of coatings have come a long way. With that; the epoxy paints aren't cheap, and they have a specific methodology for applying that Does need to be followed. Some dont play well with others; some require a specific surface prep; ect
Edit: My worry with even the nailer method; I worry you will get a Wave kinda effect between nailers; and if we are going to do 2x4 nailers, and 1.5" foam or dense glass; we might as go down to studs and build back....