Anyone care to venture into comparisons and advantages of a square sail rig on a boat of this type?
A square rig is about the best for sailing downwind.
But, when sailing upwind of say 135 degrees off the wind, the disadvantages pile up. The first is that you need at least four lines to control the sail, two sheet lines, for the bottom corners of the sail, and two brace lines, to control the angle of the yard. And this is for just sailing down wind. Sailing further up wind, you will need two tack lines, to hold the foreward corner of the sail toward the bow. You may also need bow lines, which connect at about mid-point of the sides of the sail, to keep to keep the windward side from curling inward. So, now we are up to eight lines for a single sail. If you have a lower boom, you can eliminate maybe four of them, which is what the square riggers did. They set one sail on top of another, and often strruck the lowest sail first (which didn't have a spar under it), when it breezed up.
Another problem is the yard, which has to be quite stiff (heavy per material).
A gaff or a sprit sail (the square one with a vertical sprit) will likely be best for you. These are what the working sailing barges usually carried. One of the goals should be to keep the mast as short as possible. This way, you can get beneath more bridges, and it is easier to lower the mast, when you can't. I have read stories about sailing barges getting past low bridges by quickly lowering the mast (with the sails still set!), coasting under the bridge with their momentum, then hauling the mast back up on the other side.
For minimum Sail Area, I would go with: (Length * Beam) + above water profile area. This will work unless the boat is unusually heavy for its Length and Beam.