No vac to waste, maybe looking at a "trash pump"? Need suggestions

Hi all,
Been quite a while since my last activity here. So glad this forum (and Ben) are still around!

Pool is a 17x33 inground with a Hayward DE filter.

The perennial problem is getting out the sludge in the bottom this time of year. I've kept out most of the leaves and branches with a net overwinter, but the algae I've killed with algacide is now sitting on the bottom (along with the tree debris that slipped through the net). In the past I've futilely tried to vacuum it out but it clogs the DE filter so quickly I might recharge it four or five times before it's cleared.

The Hayward doesn't really have a "vac to waste" except for the outlet valve which would deposit all the water I remove on to the lawn, which is undesirable.

I envision a trash pump (I think it's called) sitting on the deck which I could then direct to a wooded area. Does such a thing exist that pool maintainers could recommend?
I've tried a couple local tool rental places and they mostly just scratch their heads.