I may be in the minority here, but I would try really hard to stick to two naps. I know when my son was making the transition (around 15-16 months) there were definitely days he needed two and days he needed one. On days he took one, they were still pretty early (11 ish as compared to a "normal" afternoon nap time) he would go to bed really early - by about an hour earlier than usual. This is to prevent him from getting over-tired. Please really caution against getting over-tired - if he does, he will struggle even more with naps and then it will be really challenging to fix and know what he needs.
Esp because you're a SAHM and have some flexibility with his naps - this is what I would try.... For a good two weeks or so I would continue to lay him down for each nap and be consistent with trying to get him to sleep. If he wakes 30 minutes in - let him fuss and cry for a bit so he will learn to stop waking himself up at 30 minutes in. Sounds to me he's just trained himself to starts taking short naps. He's at an age he realizes when he falls asleep he is missing out on all the fun the world has to offer. If he doesn't get enough daytime sleep - put him to bed quite early at night.
If after a few weeks, you are still struggling, you could try transitioning to one nap. Just beware it will start by being like a 10 am nap (and little later every few days) and during those weeks you will need an ultra early bed time. You can see if this alleviates your problems.
I would guess that if you are consistent for a couple solid weeks with insisting on two nap days and work to retrain him to take longer naps, he will re-establish this pattern. My son has/had multiple occasions where he will challenge current sleep patterns and almost always if I am consistent in my expectations for him, he will fall back into it within a week or so. Seems to me 12 months is way young to go to one nap, but then again a huge portion of children are way under-rested and parents just tend to accept this as normal.
Good luck to you!!
PS I really recommend the book Healthy Sleep Habits, Happy Child by Marc Weissbluth. It's fantastic, based on a child's developmental needs and has been a life saver since my son was about a month old. I still refer to it all the time when a sleep challenge comes up!