It's hard to say if the change has to do with the illness, or is just a developmental change. 12 months a lot of things happen, including learning to walk etc.
The first thing I note is that he's getting about 3-4.5 hours of daytime sleep. This may be too much, giving you short nights. What I'd probably do to start is get rid of that cat nap and then move bedtime a little earlier. I know you're probably worried about having even EARLIER wake-ups, but I have a feeling that he's robbing nighttime sleep for daytime. At 12 months, we usually see only 2.5 hours of daytime sleep (1 hour nap, 1.5 hour nap) and 11.5 hours at night. He should be able to handle 4-4.5 hours of A time.
I think nap #1 can be pushed later. Even with a 5:15 waking, he's only doing 2h45 minutes of A time. So, let's slowly push that out until it's closer to 4 hours. This first nap we can push to a pretty long A time because even if he's OT we only want an hour nap out of him, so it should work out. I'd probably move by 15 minutes every day or two, depending on how he handles it. If he seems to be doing great you can increase faster.
Then Nap #2 should be about 3.5-4 hours after he wakes from nap #1. Right now you only have 2.5 hours between naps. Let's stretch that. Then that will push bedtime later than you have it now (even with a catnap) and should then help you to get a later wake-up.
Right now you're letting your child have A times that are more commensurate with a child of about 6 months old! He must be a WONDERFUL sleeper to go along with that!
The problem, as you're finding out, is that he's going to start robbing his nights to account for alllll that daytime sleep. Plus, it will make it REALLY hard to move to 1 nap as he's not even up to 3 hours A time and we need to see closer to 5 hours A time before 1 nap will work. I know it seems like this routine is fine since his naps are so nice and long, but like I said it's going to backfire -- and already is, as you see with your EW problem.
Let's pretend a 5:15 waking to start with. Go ahead and get him up so as not to complicate matters. In 2-3 days, I think that wake up should be back in the 6:15-6:30 range without too much effort. Here's what we'll start with, in terms of routine:
5:15 awake
8:30 Nap #1 (hoping for 1 hour or more)
10:00 waking
1:00 nap (hoping for around 1.5 hours. If he sleeps 2 hours that's OK for now; we may limit if EWs remain a problem)
2:30 awake
6:00 bedtime -- I realize this may be a stretch, but this will slowly get better over the next few days.
Step #2
Have him do 3h15 A time before each nap. No more than 4 hours of A time before bed, but bedtime should also be no earlier than 6.
Step #3: Have him do 3h30 A time before each nap. No more than 4 hours of A time before bed. Hopefully bedtime is closer to 6:30 or 7.
Step #4. Have him do 3h45 A time before each nap and before bed.
Step #5. Have him do 4h A time before each nap and bed.
The # of days you stay at each step depends on how your child is doing. If naps become 45 minutes or shorter it means we need to stay at the new A time for 3 days or so before changing again. If naps remain 1.5-2 hours long, go ahead and lengthen A time again by 15 minutes the next day, as illustrated above. Bedtime may be stretch for the first couple of days but after that things should get better as his wakings get later due to less daytime sleep.
Keep me posted and I'll walk you through the changes! Just so you know, LOTS of moms of textbook/angel kids get in this same situation as you. Textbooks especially show sleepy signs at roughly the same time every day, even if they are ready to stretch. At first it works OK, but eventually it starts to backfire.