With Specialized geometry and your description, the 61 should work well for your initial reach-over ride. I ride a 61 Specialized comfortably long and/or fast at my 6'-3.25" size. Certainly frame sizing is your first pass but finer fit & tuning [put 3 hours of a pro fitter price into your purchase budget] zeros it in. Obviously everything from seat tube height, seat position and slope, stem, hood and drop, crank, pedal and cleat all add up. As some already have eluded; these non-exhaustive variables can make a difference per a manufacture’s model by a couple of centimeters in frame size. When you find yourself on the cusp of frame size [with respect to your height, torso and leg proportions] the wise money includes an eyeball from a pro fitter [independent preferred] regarding the base frame size before you close the deal. Once ok and deal done then spend the 2-3 hours post purchase with that fitter to finish the tailoring. All in all, a great learning experience that takes your biking knowledge and skills to another level.
BTW. You mentioned a two hour car ride just getting to the bike for test ride. If so I would change the description of 'Local' Bike Shop to Regional 'century away' Bike Shop
