you're a few inches shorter than me but your inseam is 1.5 inches longer, so that may explain why your reach is too far to the hoods when on a 56cm frame. your lower-body may like the 54 or 56 frame, but you don't want to get a frame too big and end up going with something like a 60mm stem just to get the right reach to the hoods. in my limited experience, i've found it easier to buy one frame size smaller and then adjust the seat height and fore/aft positioning to get my lower-body properly aligned, and then see if you'll need a shorter/longer stem. i was told by the LBS that, based on my height, i "needed" a 56 or 58 cm frame, but ended up fitting perfectly on a 54. i test rode some 56 and 58 frames and then a 54 and there was no question in my mind that the larger frames just didn't fit me right.

have you taken any test rides yet? see if they have 52, 54, 56 of the same bike and try em out. they should do a quick ballpark fit for the test ride so you'll be able to see if that frame is the right size for you. in the end, go with whatever's most comfortable. if it's not comfortable, you're not gonna enjoy riding it.