Insulation, Radiant and Vapor Barriers - Preferred Method to Reconstruct Foamboard?

I bought enough 2" polystyrene to put a double layer around the perimeter of my crawlspace. This should take me to an R-20 which is the recommended level for my part of the country.

When making my purchase, I knew that it'd have to be split into at least half to get through the tiny opening into the bottom of my house, but now I see that it'll have to be cut into at least thirds and I've decided that it'd probably be easiest, if I just use the pre-scored quarter board cuts.

Because I'll be double layering, I'm now operating under the idea that I'd lay the first course horizontal and install the second layer vertically to "fence-in" the cuts. And of course, this leaves me with the question of what would be the recommended method to reattach the sections.

All I can think of right now is duct tape, spray adhesive, maybe caulk or possibly some kind of "buttered-on" spackle; Because I'm sure that I'm not the first person who'll need to reconstruct styrofoam under the house, I thought that I'd ask the more experienced people on this forum.

What is the preferred method to reconstruct the boards, while minimizing the loss of insulating value?

Thanks in Advance
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ETA: I now see that Loctite also makes a construction adhesive in a pressure pack and another adhesive specially-formulated for foamboard/ceiling tiles, but because I'll just be attaching foamboard to foamboard, I have to wonder if this would be an overkill.

2nd Edit: Further searching shows that Loctite's foamboard solution isn't unreasonably priced, but I don't know that I can buy it within a 100 miles, while I know that I can get their styro-friendly spray adhesive. I'd probably delete this post if I could, but because I can't: If the foamboard adhesive isn't your first choice, what would it be and if it's not available in my area, what would be your backup suggestion?

Thanks