Ok Honey, so generally it seems that you are in a kind of UT/OT loop. It means that you put him down too early in the morning for a nap, he does an undertired nap of 45min but after couple of naps like that he becomes OT as no proper nap behind him.
Firstly - have you looked at this link about average A times? For 3mo it's roughly 1:30 so you could try to push your DS slightly.
Average A times- BOOKMARK ME! These A times are in general after good sleep, so after night or after a proper 2x sleep cycles naps. However some kiddos could do the same A after even a short nap. So in general if you son is doing a short nap, the following A should be shorter than "standard" one, but it's up to you how much to shorten it. I have to say I have never shorted A times after crappy naps. I usually pushed for a normal A and thanks to that I was getting a mammuth nap afterwards of 2h or so. It might be an OT one but it was always easier to resettle than UT naps. Does it makes sense for you?
Regarding white noise, I am a great fun as it really saved us from the moment I found it (DS was 6wo) till the moment we weaned (6mo). Afternoon naps were always a problem here and frankly speaking, catnap or last nap of the day was so difficult to get here that I thought I have a colicky baby during first 3 months:)!