Hi there, (((hugs))) short naps are frustrating, btdt, especially with DS! The good news is that most LOs will get there eventually, but for some that's more like 6mo than 4mo, I'm sorry that's not what you want to hear, I know, so in the meantime a few thoughts/questions...
1) A common theme I've observed on here (and IME!) with 4mo is that many LOs are ready for a stretch in their A times, but will still show their tired cues at the time they're used to going to sleep. This is where we need to gently keep them up just a little longer, eg with some low key gentle activity, so they don't get wound up and OT but get just that little bit more tired so that they're more able to have a longer, restful nap. So I'd start by gently increasing that first A time, by 5mins, 15mins, whatever you feel she can manage, and hold it there for a few days and see what happens.
2) After a bad nap, the next A time will need to be shortened. Don't worry too much about getting exactly 3.5h between feeds, you can have some flexibility here if needed in order to get the next nap early enough so she's not too OT to take a good one. Here actually, I like to cheat
At this age with both of mine, I'd rely on one nice long nap in the sling every day - sometimes it would be straight through, other days not but I found they'd resettle more quickly and reliably in there. Do you have a prop like this you can use to help you get through the day? Or is this what you mean when you say you use all manner of techniques to help her get rested?
3) How does she fall asleep for naps? Do you help her or is she settling independently? (Just talking about cot naps here)
4) Hopefully as you start to extend her A time during the day and perhaps cheat (we call it APOP - accidental parenting on purpose
) a nap, you'll get that 3rd nap happening a bit later and be able to forget about fitting in a 4th nap, most 4mo LOs wouldn't have it but I do understand why you feel she needs it... If you can't resettle the 3rd nap (again, as the day stretches out you won't need to anyway) and feel she needs a 4th then I'd try it a bit sooner, ie reduce the A time after the short 3rd nap and try for another around 1.5h later, or even sooner. This might mean feeding earlier, that's ok.
5) It's ok to have a longer night than 12h, so putting her to bed earlier rather than having that 4th nap might work, if not now, then in a couple of weeks or so once the day has stretched out more. The way she is at the moment, it sounds like she's just accumulated too much A time in the day, so I'd really try to make her
A times in the late afternoon/evening as short as you can - at this age we didn't even bother with baths at BT for example with DD, as she needed really short A times after her CN and there just wasn't time, she was a slow feeder too.
I hope that gives you a starting point - how does that all sound to you?