Delay lodging the claim until after you pay the new premium (which will be higher but not because of the claim cause you haven’t lodged it yet but because insurance companies are shites).
Once you lodge it they will ask why and say you’ve said, the mechanic is busy and I couldn’t get it checked until now… they may increase the premium but likely they won’t and you’ll get at least another 11 months before they screw you on premiums…
PS: I‘d have jacked it up and put on stands to have a look underneath as a rock or stick could have jammed or bent the selector rods… if thats all, it may be an easy fix but check the rest of the gearbox thoroughly
Still with tow fees and repair, it’s likely to still be over $700