Just got off the phone with EVA.

Spent 3 weeks trying to call their local San Francisco number, finally got someone on the first try today by calling their Toronto number.
Agent was super helpful and pleasant, and walked me through the refund process. Turns out she is based in LA, but working through the Toronto office.

We were due to fly May 15th SFO - NRT and back KIX - SFO May 24th. Tickets have been cancelled, and we're losing about $200 a person due to penalties, but still able to recoup about 80% total cost.

TLDR: If you can't get through to the local US office you're trying to call- CALL TORONTO'S OFFICE INSTEAD (thank you dav662 for this info and DP!)