Your fit analysis recommends one frame size: 51 cm, measured center of bottom bracket to center of seat/top tube intersection (c-c) & 53 cm, center of bottom bracket to top of seat tube (c-t).

While the seat tube is typically how bikes are sized, it's really the top tube and overall reach that matter more because no matter how long the seat tube is (within reason), you can adjust the seat post to achieve the correct seat height. You dial in the reach of a bike by getting the stem length correct (also, stem height--in relation to the seat height--has a bearing on comfort). Most road bike stems I see are in the 100 to 120 mm range, so you can find a frame that when used in conjunction with an average stem gives you the proper reach.

To answer your question more directly, road frames are sized so close to each other (like 2 cm) that if you're really in between frame sizes, you can usually go with the smaller one and then set your handlebars in the correct position with the appropriate stem. Again, shoot for 100 to 120 mm, any more or less and you might want a different sized frame.

You're right, bike fit (not just the frame but also the stem, handlebars, crank, etc.) is very important for comfort. A general rule I use is the 45/90 method: with your handlebars an inch or two below the saddle (whatever you find comfortable) and your hands on the brake lever hoods, elbows slightly bent, back straight and your butt on the seat--your back should be about 45-degrees from horizontal and your arms should come away from your torso at about 90-degrees. For a more performance fit, achieve the same angles, but with your hands on the bar tops instead (that way, when you're in the hoods, you stretch out further).

Good luck and welcome to the road. I started off as a mountain biker, too. I'm 5'8" and ride a 54 cm fame with 55 cm top tube and 120 mm stem.