Except for the 40 hours part, OP's was exactly my experience. BigCo contracts out to some awful 3rd party that can't get their paperwork straight.
I actually got notice that my leave was "approved" (as if they could disapprove?) AFTER I returned to work, that's how bad their process sucks.
Don't even get me started about straightening out the bill for health insurance -- yeah, you have to pay your employer's share while you're on leave! Surprise! (I guess this might vary from company to company).
Better than nothing I guess, but I think I'd rather have lower taxes and just take straight PTO.
Good to know though.
Just move! Great and completely realistic solution to the problem of what to do about paternity leave within my company when a kid is on the way. Brilliant! I wish I'd thought of that.
I'm not trying to patronize you, but it sounds like you should be looking for a new job!
Edit: Here's a HN thread where I asked "where should we move to?" https://news.ycombinator.com/item?id=10103373
Hyphenated company manages to avoid our state laws on covering infertility treatment by funding its own health plan, thereby taking advantage of a loophole in the state law. I can only believe that such a large company, in the state where it is incorporated, would find ways to put loopholes in any new laws.
"Just move" isn't usually bad advice for a single person, but when you have a family, that's a whole different thing.