Yes, there IS hope! Sorry for the delay in responding but we were away for the weekend and I only had access to basics like email & FB, and even that was spotty.
3 months is a growth spurt so E and A and S times will likely be all over the map for a while. That said, that first A time is really REALLY short, and although you're following her cues, I'm thinking that if you're able to just get her back to sleep with the paci (instead of the one breast, since she doesn't seem hungry enough for a full feed yet), then try for a full (or at least longer) A time when she wakes properly for the day, that might shift things a bit. If you can get an A time - by which I mean any time not really sleeping, so even if she's not truly ACTIVE, she's *awake* - of even 1 hour 15, you're extending the A times. Then if you can get in to her while she's napping at about the 40-minute mark and wait for her to stir, you may see that she spits out her paci, which makes her wake fully. Instead, try to slip it back in before she's awake enough to notice it missing and see if she re-settles. If she does, then YAY, and if not, go thru trying to extend the next A time a little bit and try again next nap cycle. It took us a couple tries some days to get all longer naps, and some days we just didn't, but after maybe 3-4 days we were getting better at it. We had no luck with pat-shh for either of my kids, so don't feel bad if that doesn't work for you.
Hang in there - we're right here with you!