I use Chemical Guys Honeydew Snow Foam in my foam gun. I don't know if I would agree with you that it is stronger. Like it or not (and I would have to say 99% of us do NOT), Chemical Guys sales copy is about as confusing as it gets. They have a lot of products for each sales category, and consistently recommend different things for the same thing in multiple places.
For example, in one place they say the best maintenance soap is XYZ (maybe, Maxi Suds II), but in another, they say if you want a great clean that won't strip the wax, which is a maintenance soap, then go with Citrus Wash + Clear. So confusing...
So, that being said, I have only used Honeydew Snow Foam and Citrus Wash (Red) from Chemical Guys. I like Honeydew Snow Foam and will probably buy a gallon to use exclusively in my foam gun, as I prefer Optimum Car Wash, Ultima Paint Wash Plus +, and a few other "boutique" shampoos and soaps in the bucket.
Check the Chemical Guys chart to see which soap is the highest foaming. All of the ones you are considering will work in the foam gun, however only Honeydew Snow Foam can say (at least CG says) that it was designed for the foam gun. The others can't say that, at least yet, you know, until Chemical Guys releases another soap product and changes all the soaps copy.
My vote: Honeydew Snow Foam.
Happy detailing!