I own a Big Block and while I typically ride a 58cm, All City calls the size I have a 55cm and it fits similarly to my 58cm or 23" bikes. Based on your height, which is only one factor, but an important one, I'd say the 52cm should work for you.
My assessment of bike fit is not based on stand over height as much as top tube length. The reasoning is I care more about how it feels when I'm riding it, compared to how much clearance there is when astride it. I don't do that very often.
My experience with the Big Block is 100% positive. Good luck and I'm sure you'll love it!