Too many Amex cards too soon has triggered F/R for some in the past. However Amex generally likes to approve for existing card members from what I used to read. If your income/expendable cash can easily support overall credit lines the F/R is only an annoyance. (carry a back up card besides your Amex card as F/Rs tend to freeze cards until completed). F/R if happens is pretty much a phone call and a fax of financial info, ect, then cards are reinstated.
As to apping all in once day... Used to be an advantage when inqs didn't update, now they seem to update right away. The advantage would be new accounts if approved won't be reflected for usually 30 days. So actually you have a 30 day window advantage. Of course it's possible if someone sees a bunch of inqs on one day they may assume you were denied and assume you won't have other cards on the way. That is a far guess at best.
If you app to banks that check a different credit reports (TU, Exp or Equifax), they won't see each others inq. 
No time restrictions that way.
There are also mirror servers, at least last year there was, that sometimes don't update instantly. So while your inq may post to one, it might not be reflected on all instantly, which may give the edge you are questioning a
Score drops with each CC inq up to the max amount of point loss. Point loss stays for 12 months with inq's.
If you are carrying debt with Discover, let it update to a "smaller amount" before applying for maxium results.
+1
congrats on the approvals
GL with the new TLs!
keep in mind any additional app in short time period can increase further the likelihood of AA and so is inadvisable.
7 apps at once incl 2 amex revolvers can be risky business in today's climate. YMMV.
Congrats on the new trade lines.
On the other hand.... AOR = AA, plain and simple.
