Have you done the Know your baby quiz? I wonder if she is just a grumpy baby and this crying before naps i s just part of her character? Really I am racking my brains for other reasons for her crying when you have been running a consistent routine, with suitable A times, and it's not even like you are trying to break a prop habit which I'd expect crying with, she is crying even in arms.
Do you ever go into her room when it is not sleep time? For instance taking her in whilst you put laundry away or vacuum or tidy up etc? How does she respond to going upstairs and into her room when it is not nap time?
For now honey I just want to reassure you that you are doing everything you can, don't take it personally that she's crying, she clearly has a lot to tell you about!! Stay calm throughout (some people find ear plugs help - you can still hear your baby but it can take the edge off and help you stay calm), respond to her crying by doing as you are, holding, shush/pat or rocking etc. And be kind to yourself, this is not your 'fault' and you are doing really well.
One thing you might try - take her upstairs earlier than nap time (so she is definitely not OT or about to cry) and see if she remains calm. If she remains relatively content put her down in her cot, say 'sleepy time call if you need me', and leave the room. If/when she cries go back in and pick up, do your usual to sooth her. I know I am slightly contradicting my previous advice to try the nap a touch later, but I'd like to see how she responds with almost no WD, just upstairs, in the room, super fast cuddle and into bed.
Is she eating ok?
Is the temperature much different between one room and another (ie colder in her bedroom?)