Drill it out and put a thread insert in. The hole location will be in the same place, you can still use a 1/4-20 bolt.

Use loctite on the insert so it's thouroughly attached to the backing plate and put anti sieze compound on the 1/4-20 bolt before you bolt it all back together.

You'll have to slap a little resin on the transom where you drilled oversize for the insert but it'll pretty much all be covered up by the gudgeon anyway