I'll discuss the situation with my employer and work out a strategy.
It’s indeed a strange situation. Everything I read here matched my understanding, and immigration even confirmed via email that I can apply for an extension based on retirement. Even the IO today said, "come back to the same counter," which implies the counter for extensions, not new visas. However, he also clearly stated that I have to leave Thailand and return as a tourist.
Anyway, we'll find a solution. Thanks
@T**
for all your help!