9wks, won't fall asleep until 2-3am

Our baby is 9 weeks old today and for the last two weeks she's refused to fall asleep until 1am-3am. She then sleeps well until mid-afternoon (e.g. just wakes up to feed at 5am, 8am, 11am, 2pm), but then refuses to nap and gets crankier and crankier all evening, so we end up spending every late afternoon and evening/night holding her, feeding her, rocking her, giving her a bath, massaging, walking around the bedroom with just a nightlight on, swaddling her, etc. but nothing seems to get her to fall asleep completely - often she'll close her eyes and start breathing deeply but when we put her in her crib (or even if we keep her laying on us), 10-15 minutes later she wakes up and starts crying again.

I've tried to keep her awake in the morning, thinking that she must have her days and nights mixed up, but if I try to keep her from sleeping she cries until I leave her alone and then she's fast asleep again.

We thought it might be silent reflux since she almost never spits up but sometimes seems to have stuff gurgling up in the back of her throat, but she hates the medicine the doctor prescribed (Infant Gaviscon) and spits it all out when we give it to her (and cries harder), so we stopped after a few days since it didn't seem to be doing anything but making her mad.

She's perfectly healthy and gaining weight, filling diapers, no fever.

Does anyone have any advice for how to get her to go to sleep earlier?