I've been told I need a "B" but may start with an "L" depending on availability, which I'm told won't matter.

I've also been told it could be "as fast as 6-8 weeks" (by relocation firm) or "at least 3-4 months unless we're lucky" (by corporate HR).

Are there other Americans (vastly different for each country AFAIK) who have gone thru this recently and if so, how long did it take?

I went through this circa 6 years ago. I started off on an L Permit (which can be the norm for many US citizens on permanent contracts, although there may be a few lucky ones here and there). I moved on to a B 2 years later and I just got my C Permit a few months ago.

It took about 2-3 weeks to get my initial L Permit.

2mos exactly

My papers were submitted to the cantons TEN weeks ago, and I'm still waiting. Apparently, it was held up at the canton level for 7 weeks (I'm told this is quite rare, though). Now it's been in Bern for the past three weeks, and I'm still waiting to hear back for my B permit application.

Thank you for the above comments about the "L" permit. I'll bring that possible option up with my boss if this one doesn't come through.

Best of luck to you with your permit!