I am not here every single day so bare with me
If he is in pain due to teething and discomfort due to his cold it's very difficult to tweak anything, and IMO what you see now is a result of him feeling poorly.
I do think you should wait a few days till he feels better and then you would need to start and work on his A times. You are right that he is in an UT/OT loop or so it seems and the only way to tackle that is by tweaking the A.
I think that he is UT for his first naps because it sounds like he often wakes up after 45min happy and needs resettling. 45min naps usually indicate UT. So the way you increase the A to prevent OT and also to give him enough time to get used to a new A is by increasing it by 10-15min every 3-4 days and if nap is still UT you go ahead and increase it again. What you are aiming for is a 1.5h nap, at least. It's very important that on the days you are increasing the A you are very consistent with the A, so if you up it to 2.5h you keep doing that for four days, not 2:25 and not 2:35. I know it sounds strict but if you want us to really know what's going on then you have to be.
I don't mean to be too harsh, but it seems like right now there is no consistency with the A and you won't be able to figure his A if every day his A is different. I refer to the first A because the others are anyway in daycare and grandma's so if we figure what is the right first A it will be easier for us to figure the rest of the day.
He is not well right now, but in a few days when you start tweaking the A and when we get things right I believe your nights will not be a mess anymore. Good naps day = a good night sleep, for most babies of course.
How old is he now? There is a GS at 6 months so he would want to feed more when he hits that. Is he on solids already?
