Sorry it's been awhile since I've been on the forum.
I tried to change the APN settings manually but had no luck. iMessage sends instant notifications for a short while after I restart my phone or turn Airplane mode off/on. But, it shortly reverts back to its old, devilish self.
I think it's interesting that jeffla mentioned people on Verizon who were having the same problems. So, this makes me wonder... Is it Apple's problem with iOS 7.0.3 in which case 7.0.4 (which I upgraded to today) should fix it? I would think that there would've been more, bigger discussions about this already, but so far, we're the only 5 that have the problem (or so I've read... or not read).
Like I said above, I upgraded to iOS 7.0.4 today and hopefully that'll fix the problem. I haven't noticed a delay in any of my other applications, which is why I'm holding out hope for iMessage, but that doesn't mean they're not there.
I still have my old 4S and I'm considering going back to it until this is fixed (even though I will greatly miss LTE and the A6 : ( )
Only time will tell, I guess.