I, like others, think the shoes are too flexible and or too narrow, so you can test the narrowness somewhat by loosening up the straps or ties and open the shoe to as wide as they will get the go riding and see what happens. But I'm leaning more towards the shoe not being stiff enough, and a 7 (depending on how that particular manufacturer determines a 7 over another manufacturer's 7, they are not all the same!) isn't all that stiff.
What you can try doing is swapping the pedals off your old bike and wear your old shoes to see if the problem reoccurs; if not then try to see if you can get Look cleats to fit your old shoes, then test ride and see if the cramping occurs, if not then it's the new shoes, either they're too narrow or not stiff enough or a combination of both.
The other problem could be the pedal isn't large enough for adequate support for the shoe which again would make it important to have a really stiff shoe.
Another issue could be the cleat position, I know you moved it around, but ideally the ball of the foot should be centered with the spindle of the pedal, not getting that right will cause the foot to flex and cause cramping.
http://www.stevehoggbikefitting.com/bikefit/2011/04/power-to-the-pedal-cleat-position/
https://bikedynamics.co.uk/guidelines.htm#1
https://wheel-easy.org.uk/wp-content/uploads/bike-set-up-2017a.pdf
The other problems, which probably aren't likely since this is a new problem, but make sure your hydrated; another weird thing you can do, and it's cheap to do, is to drink about 2 to 3 ounces of dill pickle juice, then wait an hour the go riding, if the cramps go away then you have a unbalanced electrolyte thing going on. The pickle test is cheap to do so something you might want to try, but don't try it and also experiment with the pedals and shoe, experiment with one thing at a time.