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Ruben-- Amazing work so far. Those little joining strips are incredible!
You mustn't worry too much about gaps. The map is not so accurate that seams could join perfectly everywhere. Also, where mountain ridges are (such as the Andes, near you?), you'll be accessing this "white space" to fashion your joint, exaggerating the surface topography to mold peaks and ridges.
As for cutting the map into two or three pieces -- good luck. Never tried it myself. Sounds like it might be a useful trick. And it will give you better access to the developing globe's underside. I found this inside-out view to be enlightening, and might prove useful in designing the various joints and seams.
As for additional joining strips, do indeed think (note the "k", not a "g" in think; you are using "thing" when you obviously mean "think") carefully about where you want them. There are several places (not sure where at the moment) where these would be appropriate -- places that are "colder" than others.
"Dovetail joints" is a very nice term as well. The mid-ocean ridge, the only one wherein I designed the joinery system (the orange flaps), is intended to assemble this way. A bit like interweaving your fingers together. Note that the mid-ocean ridge is the earth's loosest seam.
As for Zathros's comment, the most stable plate, relative to the others, is Africa. But I've never envisioned the assembled map as being able to portray great relative movement of plates, that is, one sliding over another as you often see in those animations of how the continents used to be connected, and where they will be in several hundred million years into the future. This is NOT that globe!
Indeed, I'm an adherent of geomorphologist Paul Lowman's fixed continent theory, wherein the continents are pretty much where they've always been. The "pretty much" qualifier is significant, in that it allows for small-scale shifting and reshaping, but rules out the huge transformations usually depicted when the continents are imagined as thin rafts loosely connected to the mantle. Paul points out that recent results of seismic tomography show that continents are much thicker than we once imagined, with roots extending down on the order of several hundred miles, or almost the thickness of the mantle itself.
Note to Ruben -- this gives you lots of room there on the continental undersides to fashion some intricate paper engineering normal (90 degrees, the up-and-down direction) to the surface. Save the "white" parts of the map!
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