Ok sorry, I guess I got confused when you said he sometimes goes down at 1.30pm or 2pm, but you always put him down at 1pm, right? I think I'd probably start by putting him down a little later, since he seems to be struggling to settle at 1pm consistently now, is that right? With my DS (nowhere near this stage with DD yet!) even 15mins later could make a big difference to his settling and often result in him actually falling asleep earlier than he would have done had I put him down at the old time - if that makes sense? So perhaps try putting him down at 1:15 and see if that makes any difference? An A time of around 6h before the nap would be quite common so I'd expect you to need to push the nap later at some point anyway.
If he has a day like the one you posted, with nap exactly 1-3:30, what time do you put him down for BT? Do you put him down at 8pm but it sometimes takes an hour for him to fall asleep? Or is it only if he ends up napping more like 1:30-4:30 that BT gets that late? Just trying to gauge what happens with different length and times of naps. If he's asleep by 8pm with a 1-3:30 nap then I'd say that's fine.
What I'd find with DS is that if he started to struggle with settling for his nap, I'd push it back by 15mins (keeping same length and same BT, initially); but if he started struggling to settle at BT, I'd put him down for that 15mins later. At some point that would make the nights too short (for him, anything less than 11h would make him tired the following morning - yours may prefer a different night length?), so then I'd shave 15mins off his nap instead and bring BT forward by 15mins initially (since he'd be more tired from the shorter nap), and then BT would gradually get later again until it was time to shave a further 15mins from the nap. It seemed to work for us so perhaps you would find a similar strategy useful?
