Wood bleach? Teak cleaner?
If you can find them, both are mostly oxalic acid.
OR -
How about electrolysis ?
The frame submerged in a solution of water / washing soda, an old car battery, a battery charger, some copper wire, a cathode (steel plate, rebar, etc), and Bob's yer uncle:

Rust removal by electrolysis

https://www.garagejournal.com/forum/...d.php?t=154196