Unless things have changed recently, only the very first extension counts as a 90 day report and gets you a slip in your passport with the next reporting date. After that, extension dates and 90 day report dates are generally not connected to each other. (I say "generally" because I have heard of immigration occasionally doing the report when someone comes in for an extension, but that's not the general practice.)
Totally agree, I've been very happy with it - it's made life much less stressful, and being able to use Fast Track makes travel really easy. But I'm still amazed at how many staff still haven't gotten that memo!
I know. What I'm saying is that an officially certified copy like the one in the photo can be "chain authenticated" using the procedure I described in order to be usable for any official purpose. The certified copy from the county could generally be used "as is" almost anywhere in the US (other than some court proceedings), but some authorities can and do insist on the fully authenticated version.