If I could not source an appropriate brace and bit my second choice would be one of the new generation 'Impact Drivers' sold at home centers in the cordless tool section. Impact drivers install and remove fasteners with a surprisingly gentle impact hammering. We have been using them for over a decade to install/remove many varieties of fasteners including screws.
The do no damage to screw heads if appropriately sized. You can get a set of slotted screw tips and modify to fit your screw. It really helps if you have a friend who is a machinist or retired one that can restore the temper through a simple heat treatment process called oil quenching after you modify to fit.
Good luck