Copy. Looking at your schematic gives me questions on the physical plumbing. Im using my phone and cant zoom in on your pics. With the size pump you have head room isnt an issue getting water up to your skimmer. The return being gravity will be out paced by your pump. Unless your drain is over 3". A return pump would be what i do. Its similar to how a negitive edge is pumped on a pool. Also if ypu put a dc pump you can play with the return via remote
The bead filter is all closed loop, no gravity drain. So it should balance.
I’m adding a separate sump system, but that post filter and not pressurized.