We are having this exact same issue with our DD who is the same age. I was actually just about to post a similar question, so I was happy to see your question here. For the past couple of days she has only napped 45 minutes at a time which, as you know, throws the whole day off. I am in the process of trying to extend her A time by 15-20 minutes or so, even if she is showing me very visible signs that she is tired. I'll let you know how it goes! She has had naps as recently as 5 days ago that have been the standard 1.5-2 hours (and I haven't had to intervene at the 45 minute mark), so I know she is capable of doing it...I think it's just a matter of striking that balance between UT and OT. It's tough, especially when they wake up from a short nap SO awake!
As far as reading to sleep goes, you may want to look at moving reading further up in her wind down time, so she can still associate drowsiness with it, but not be dependent on it to sleep. Perhaps follow it with a few minutes of sitting quietly in the dark and then put her down awake. I speak from experience as a fellow prop-to-sleeper (in our case it was nursing), it isn't easy at first but they do eventually get the hang of it, and from everything I've read on this forum, the sooner you can teach them to fall sleep on their own, the better. Shush-pat has definitely helped us in this transition! But as Lindsay27 said, there is likely no harm in reading to her now...just be aware that it
could become a prop.
Keep us posted on how she does with napping and the extended A times!