I don't mind helping out with the hot weather, this is better than other options.
Failing mid length is a good indicator the basement is adequate, as is the base rock. This is where I'd expect to see exp cont creep.
How about trying two cross cut cleats first at 250' from the bottom, the second 50' further up the hill. if 30" deep it would be only a couple yards.
If you use the 8", or 12" wide trench and increase the styrofoam to 1" thickness, scratch it down 1" and apply sealant to form a 1" wide x 1" tall slug of sealant all the way across.
The material needs to be elastomeric and able the stretch and compress (much like a motor mount.
If per chance that "crack" is widening in the 50' section and the base was smoothly graded before the concrete was poured, one might be able to saw cut the 5' wide ribbon in half or thirds and with a big azz excavator (with street pads or lumber) to cross drive pull the slabs back together (before the cleats are poured. Of course any material in the crack needs to be mostly removed before "sliding" in together and reseal any cuts and e.j.'s similar to the above.
The thing with most (all?) elastomers is the depth should always be kept to the width of joint or the material will shear at the face of concrete(woor, glass, whatever material is being sealed). This is why backer or sand should always decrease depth of sealant.
p.s. sorry for any typos..... I noticed a bunch above..