I have started to work on nap training with my 5.5 month old and I'm having SO much trouble with nap #3. I need advice!!

I'm doing CIO w/out checks unless he is REALLY freaking out (we did it with checks for night-time and it worked well, but for naps it seems to just disrupt things.

Here's how today went:
6:00 wake-up
7:08 Put Down for Nap #1 - fussed for 40 minutes, slept for 40 minutes
8:35 Wake Up
10:30 Put Down for Nap #2 - cried for 20 minutes, slept for 90 minutes
12:23 Wake Up
2:25 Put Down for Nap #3 - Laid quietly for 10 minutes, then started crying. Cried for 45 minutes. Nap Fail.
3:30 Got him up. Played quietly for a few minutes, changed diaper, topped him off.
4:00 Put Down for 2nd attempt at Nap #3 - cried 30 minutes, slept 30 minutes.
5:00 Wake Up
6:45 Bedtime - went right to sleep

He still wakes up twice for night feedings and is an early riser - usually around 5:00 am. He's getting 9.5-10 hours of night time sleep. Because he is an early riser and his naps are short, I would think that he DEFINITELY still needs 3 naps, but that third nap is SOOOO hard. Would you do anything differently?