The 56 sounds like a better choice.

I’m 5’11” with a 33.5” cycling inseam. For the past 8 years or so I have ridden a size 56 bike. Because it is compact, I’m able to use a 12 cm stem and also am able to raise my seatpost up higher. It looks proportional according to the sensibilities of the past 10 years or more.

Back in the day (mid 1970’s to mid 1990’s and beyond) it was not unheard of to want a bigger frame like a 58 to a 62-ish size. My Puch Marco Polo is sized as a 25” (center to top) and is quite comfortable for long, touring type rides. The need to drop the seatpost low, combined with a short 8cm stem does lead to some rather boring geometry for fast club type rides with today’s fast riders. Climbing is one of the big deficits of a too big bike. At least for me. I really love the tossable feel of a compact frame. Smaller frames are a little more squirrel-y but I think the adaptation is made in like two or three rides. Now with that said my 25” puch has a road triple combined with a generous range on my freewheel making long steep climbs perfectly passable. But as I said, the big frame is just not very nimble climbing, thanks to the top bar impinging on some of the side to side motion that I favor (when called for out of the saddle).

My new (used) road bike is an even more compact size “54”. I wanted to try it as an experiment to see if I would like it, and I must say that so far - I like it!

A few component choices will make your fitting to a 56 feel a bit better, the main one being the use of shallow drop bars. Personally, I set the hood tops of my STI levers near horizontal as opposed to the tilted up position that many folks use. For me it is plenty comfortable, especially when riding in the drops. Same for the bottoms of the drops. I set them halfway between horizontal and in-line with the rear axle. Tilted up any more and I feel it is not safe for serious descending.

Be sure to give us an update and post a picture once you pick up your new size 56 bike, OK?

Now that does look silly!
Tim