Other commenters have expert suggestions far beyond my own unhandiness. And it's been a couple of days: maybe you've unscrewed yourself already.
But if not, and you want to try the extraction pliers route, I've had good luck in several cases with this VAMPLIERS model. (Plus the name is pretty cool.)
https://www.amazon.com/dp/B006YJKAPQ?ref_=ppx_hzsearch_conn_dt_b_fed_asin_title_2&th=1
VAMPLIERS 6.25" Stripped Screw Extractor Pliers. Made in Japan. Time-Saving Screw Removal Tool Quickly Extracts Rusted, Stuck, Damaged Screws & Fasteners. - Screw Extractor - Amazon.com
VAMPLIERS 6.25" Stripped Screw Extractor Pliers. Made in Japan. Time-Saving Screw Removal Tool Quickly Extracts Rusted, Stuck, Damaged Screws & Fasteners. - Screw Extractor - Amazon.com
