Took me a while but I wanted to follow up on this in case some other people find themselves in my position.
The screw extractor worked like a charm. Heated it up to melting temp and pulled it out using the extractor and a crescent wrench.
Specifically #1 (smallest one) in this pack (https://www.homedepot.ca/en/home/p.spiral-screw-extractor-set-5-piece.1000656313.html)
Was meant for a 1/8" - 9/64" hole.
A couple of notes:
- The extracter transfers heat well, so watch that - gets hot quickly.
- Remove the brass as soon as you can. It will stick on the end of the extractor if you leave it (melted plastic/shrinkage)