Whenever you find yourself in a situation where a server cannot be rebooted, you ought to question how you have things set up. Amazon has their Elastic IP product specifically for this purpose. I'd recommend that you get that set up.
Regarding your snapshot, I'd be very hard pressed to believe you'll be able to do this. Even if it were possible to restore a snapshot to a running system, the operating system would not survive that without crashing. You're either going to need to fix the PHP issues or you'll need to swallow your pride and just deal with a bit of downtime.
To ensure your downtime is as short as possible, shorten the TTL of the DNS record for this host to 60 seconds or something like that. This will ensure that DNS resolvers won't cache the record for too long. When you're ready, take down the server, restore the snap, fire up a new instance, and re-configure your DNS to point to the elastic IP.