Re: Going onto DW's employers health covg...
I had a similar, but not identical, situation earlier this year.* For me the gap was between my employee insurance and my COBRA insurance.* There was a period of almost a month between being employed and getting the COBRA forms, filling them out, and submitting them.* The insurance and HR people swore that the coverage would be effective with no gap, retroactive to my last day of work, if I made the first payment on time.* I had to pay for that month's insurance after the fact, but that's only fair.* I was told that claims might be initially rejected for that month, but resubmission a while later should take care of it.* It turns out I didn't have to make any claims during that month, so I can't really say whether it would have worked as the HR people told me. I'm switching over to my wife's insurance at the end of the year during open enrollment.
I would suggest that your wife get on the phone (or e-mail) with HR and get a statement from them saying that your coverage will begin on Sept 6.* And I would have her submit the paperwork without the HIPAA certificate, and then follow that up with the certificate when it is issued by your old employer.* Let us know how it works out.