This suggests that I would have to position the jack 4"-6" away

In practice, they'll find a way past each other. In extremis, you
could put down a few bricks either side with a board across, and sit
the jack on that.

Hiring a cement mixer and making up loads of cement is also likely to be
expensive by the time all the materials have been costed in.

Not really, compared to postcrete.

some kind of framework (or find a 200mm+ diameter pipe) and fill in around
that, thus avoiding the filling in and digging out of the central hole.

You'll just end up with a heavy post that way - it won't be tight up
against undisturbed ground. One good shove (or high wind) and it'll
displace the in-filled ground around it.