I think your system might work.
But don't bother making it HPA.
I think for al your roots to get really wet, you need your pump to run for a minute or so.
Then turn it off and wait for example 5 minutes before turning it on again.
Perhaps even 2 or 3 misters around your roots. Misters cost nothing.
I said it might work, but perhaps not.
It is a bit similair to the system with the white fence posts that some people use.
But you use buckets.