Long allen key into the mech securing bolt and use that to get the leverage to readjust.
Inelegant, but probably something I'd try on my own bike if it wasn't too precious.
...
Unless it is too late - DO NOT DO THIS.
9pm. I was at the roadside on a dark and rainy night. Mech went into spokes, 30mph rear locked wheel. Chain locked taut. Spoke under major tension.
Only recovery was to remove the mech from the bike. Chain too tight to risk splitting.
Straightened spoke. Re-trued wheel.
Replaced mech. Hanger obviously bent.
Only solution was the allen key. Hanger is now straight, but the hole is oval and not properly threaded. I've had to replace the mech with one that has a big nut on the back instead of bolting directly into the hanger.