Honestly, I would say that the napping is definitely whats causing his night wakings. He should actually be on 3 naps - 2 naps of 1-1.5hrs long and a catnap starting no later than 5:30pm... He is extremely overtired and a 30min nap is actually not even considered to be restorative enough for him to last another 2.5hrs.
If it were me, I would look at changing his routine a little and maybe aim for something like this:
The A time of 2.25hrs (which is the av for a 6mo is based on them taking a solid 1+hrs of nap. Any less and the A time should be decreased). The morning A time is usually less than other A times and the last A time (before bedtime) is also usually less.
7am - wake and play
9am - nap 1 (in cot & drowsy/asleep at the end of the A time, which is 2hrs in the morning).
10-10.30am - wakes up from nap
12.30-12.45 - afternoon nap (in cot/asleep at the end of the A time, which is approx 2.25-2.5hrs)
2ish - wakes from nap
4.30-5pm - catnap (usually around 45mins)
7ish - bedtime
If he wakes early from the morning or afternoon nap and you cannot successfully get him through the next cycle, then I would be bringing the naps & bedtime up by 30mins.
I can understand what you are saying about him "acting" happy but all those nightwakings are from overtiredness and he really needs to be napping a little more than what he is at the moment. I actually found that after 5 months, it was a combination of reading cues and looking at the clock. Cues can be quiet hard to read in some babies and I would put mine down to sleep when her A time was up.
I would also try and encourage naps in a cot (as inconveniet as it may seem) but I have found that after 4 months, Jasmine used to get quiet stimulated by outside noises/lights so I made sure she had a dark and quiet (well we have a fan on) room to sleep in. If you have to run errands, try to do it between his napping and you can always have him take the last nap (catnap) in the ar/stroller/ wherever. Of course not all naps need to be in a cot but I don't think you can have him take a 1hr nap in a chair, iykwim...
Let me know what you think
Layla