One of the downsides of DE filters is they clean so well they have problems with getting dirty trying to clean up an algae bloom. If the pool is still green, you haven't killed the algae yet.

Two ideas:

Have you cleaned the grid by soaking in whatever the manufacturer recommends? The grid can get dirty enough that routine brushing won't clear it up.

Are you sure you are adding enough DE after you backwash? Not adding enough DE will cause the filter to clog, and backwashing won't clear it.

As long as the algae is alive, there is no end to what the filter has to remove. Getting the algae killed is the first step, and if you have to run the filter on recirculate until that happens, that's okay.