If you guys rely on my knowledge of early seventeenth-century rigging, you'll be making a big mistake. That's not my primary field of interest.
There are plenty of gaps in everybody's knowledge of the subject. I have no idea how common the use of multiple staves on the lower shrouds was. I do know that, until sometime early in the nineteenth century, just about every ship had futtock staves. A futtock stave (or staff) is a wood or iron bar that's seized to the lower shrouds under the top platform (generally as far below the top as the lower masthead is above it). The futtock shrouds run between the top and the futtock stave. Another set of lines, called catharpins, runs between the futtock stays. The catherpins have the function of pulling the port and starboard shrouds closer together, giving the yard a little more room to swing.
Seventeenth century ships sometimes had lower catharpins. Another stave was lashed to the shrouds some distance down from the futtock stave, and another set of catharpins ran between the port and starboard lower futtock staves.
I don't know whether the Mayflower had lower catharpins or not. My guess is that she had upper ones.
Just why William Baker incorporated all those staves into his rigging plan for the Mayflower II I don't know, but I'm sure he had good reasons.
Seventeenth-, eighteenth-, and nineteenth-century documents show all sorts of variations on the theme of only running a few ratlines all the way across the gang of shrouds. Sometimes they don't all reach the foremost shroud; sometimes the aftermost; there's little consistency. I've never been able to figure out just why it was done that way. The best explanation I've heard was given to me by the chief rigger at Mystic Seaport many years ago. He said most of the ratlines of the Charles W. Morgan didn't extend to the foremost shrouds, because those shrouds were often slacked off when the ship was working to windward - again, to let the lower yards swing a little further around.
I think a little terminology needs to be clarified. The shrouds are the heavy, vertical lines that run between the channels and the masthead. They are crossed by the much lighter ratlines, which form ladders for men going aloft. The footropes hang below the yards; the sailors stand on the footropes while working on the square sails. Footropes are visible in several photos of the Mayflower II, but they're anachronisms. The footrope didn't appear until well into the seventeenth century - and wasn't in universal use until shortly before 1700. Until that time, the sailors had to crawl out on top of the yard.
I think that was a consideration in the odd way topsails were furled in the seventeenth century. Crawling out on those little topsail yards would be a mighty dangerous activity. (I'm not sure the topsail yards of the Susan Constant replica could take the weight of several human beings doing that.) I suspect the topsails were furled by men standing in the tops.
Every full-sized replica of a sixteenth- or seventeenth-century ship I've seen has footropes. Authenticity isn't as important as twenty-first-century hospital bills. But a model of the Mayflower shouldn't have footropes.
The term mast band properly applies to a wood or iron band around the mast. The Mayflower II has wooldings, which are made out of rope. The function of both wooldings and mast bands is to bind together the several long pieces of wood that form the mast. If a mast is made of one tree trunk, the wooldings probably wouldn't be necessary. (I recall that when the Elizabeth II, the full-size replica of the ship that brought the first settlers to North Carolina in 1584, was built, the builders managed to find a nice, straight, fat, well-seasoned phone pole and made the mainmast out of it. But a mast made in one piece would have been unusual.)