You sound like you have a classic Touchy child. When he's a bit older and if he still shows touchy tendencies I *highly* recommend the book "The Highly Sensitive Child" by Elaine Aron. In fact, you may just want to check that book out from the library now as I do believe she addresses babies in the book. Touchies take in *too* much information -- EVERYTHING has equal importance to their senses which as you can imagine is quickly overwhelming! Imagine if the washing machine in the background, the cars whooshing outside your window and your DH talking to you were all equal in importance to your ears. Prety soon *you'd* be crying too! LOL! So, the main thing with touchies like this is to make their environment as simple as possible. While awake, only 1 toy at a time and minimize interaction with light/sound toys. It's best to let them just sit in a high chair and look out the window for example, or give them a basket with (safe) items from the outdoors to touch and feel at their own pace. It's absolutely normal for him not to show interest in anything for more than 5 minutes. This attention span will slowly lengthen a little bit each month. You probably won't see an appreciable difference in attention span until around 18 months, so for now just do your best to give him calm things to do/see. Sometimes even books can be overwhelming to Touchies so really honor his cues -- if you see him bury his head in your chest or turn his face away, stop what you're doing! He's overwhelmed.
Now for the routine!
Your first nap may be a tad too early which is why it's sort of up for grabs whether it's a longish or shortish nap. At this age 3 hours is a pretty good A time so I might slowly lengthen A1 to 3 hours and see if that makes the nap more consistent. Especially after a good solid night's sleep he may be able to handle more A time.
Now A2 I'm not sure. Looks like you're doing 3 hours. A 35 minute nap at my house was always UT, and since you only occasionally get him to resettle I suspect that may be what's up. So I might try extending to 3h15 (again, slowly!) and see how that works for him. Now, if he's seems super exhausted by 3 hours then that means he's OT so in that case let's back up to 2h45. I can't tell you for sure whether nap2 is short from being OT or UT because the 2 can often look very similar. So some of it is instinct, some of it is experimentation. Whichever way you choose to go (longer or shorter A time) stick wtih it for 3 days before deciding it's not working. Touchies esp. need some time to get use to changes in A time b/c they are just so super sensitive to shifts in their routine.
We usually drop cat naps at around 6 or 7 months old, so that is going to be our goal. If we can get nap #2 to be 1.5 hours or more than that will work! If not, then I supposed we need to keep cat nap. The fact that he's so tired by bedtime tells me that your little guy is overwhelmed by his day and that's something you're going to want to keep in mind for future: A times will probably get progressively SHORTER as the day goes on, rather than LONGER like it does for the majority of kids. My LO is that way too (he's also a touchy!) and even at age 3.5 he can only handle about 4-4.5 hours A time post nap even tho he can do as much as 6 pre-nap.
so, let's play around a bit! Lengthen A1 by 15 minutes, either lengthen or shorten A2 by 15 minutes depending on your mommy instincts, and then we'll see if we can't get that cat nap to hit the road which I actually think will make the last A of the day go better. Touchies can get pretty grumpy with a short sleep like that -- it's not enough to feel rested and so they wake up feeling disoriented and irritated.
Hope that helps! I have a Touchy as well and let me tell you these children are a gift. They are SO observant, nothing escapes their attention! As he gets older you will marvel at the things he notices. My son wakes up every morning and before he enters the Family Room he does a little mental catalogue to see what is different. One book out of the 50 we keep in there is moved and he notices!
Unfortunately, this means they can be a bit difficult to understand before they talk, so it takes a really observant parent to see what works for them sleep wise. This means it is time to take an inventory of his sleep situation and decide if there's anything that might make him uncomfortable. In our household my DH is a natural at this b/c he is also a Sensitive person (there's also a book by that some author above about Highly Sensitive People (adults) that you can check out; she also has a website and you can see if you or your DH qualify!). At any rate, you or DH or both should just look at how LO sleeps and if anything could be bothering/disrupting him during the day. Possibilities:
1) Too hot/cold. Solution: more or less clothing, heather or a/c to make temp constant
2) Too much light. Solution: blackout curtains
3) Fabric too itchy/tags bothering him. Solution make sure all tags removed and only soft clothing next to skin while sleeping or naked
4) Household sounds too loud. Solution: white noise!
Those are just some ideas so just put yourself in his skin and see what you come up with!