The Amira's a racing bike. The Madone (H3?) is designed to be slightly more relaxed. For what you want to do, I'd be looking at the Amira more than the Madone, especially if you say it fits perfectly.

Those tiny differences can make a lot of difference in comfort. Unless you've got a fantastic fitter, the only way to really know is to ride them.
And yes, I have this problem with some shops. Not a lot of demand for a 54cm WSD bike, apparently. I'm not going to buy something without trying it out, but if I have to buy it to try it out, no thanks!