My insulation theory, take a look.

A good contractor wouldn't have any problems spraying a low expansion foam into the lower section; I suggest you look around for another contractor. If everything is open as you show in your second photo, expansion is not an issue since there is plenty of room for the foam to expand. Any over-expansion is easily trimmed off. In fact, over-expansion will ensure all the space is filled.

That post hole filler uses foam that is too dense for insulation. The electric/irrigation utility I retired from used foam to set poles, mostly streetlight poles. The foam they used was pretty nasty stuff and was definitely dense. It's also pretty high expansion.