Trying to remove the stock header from the D17 head on my girls car and the far right
nut is stripped to all hell and there's extremely little room to get any kind of leverage
on it with a nut extracting socket.

There's no way I can fit a hammer or anything useful in to knock it in further.
I would try a chisel but I don't want to risk damaging or bending the bolt on
the head while I pound on it as it'd have to be hit from above rather than straight on.

Any suggestions?

 

Dremel with a cutting wheel should work.