For treating that amount of water at one time, I'd recommend one of the higher-volume gravity filters; the two that I'm familiar with are the Platypus GravityWorks and the MSR Autoflow. (The filter element is identical in each - both are Cascade Designs companies - but the dirty water bags are different.) I've used both, and both are fast and easily backflushed. You can hang up to four liters of water to filter, then walk away to do something else (as long as you're filtering into a 4-liter clean bottle; otherwise, you have to tend it to change smaller containers as they fill up.) Both of the bags are wide open at the bottom and easy to scoop and fill - the Platypus uses a ziploc-style closure; the MSR uses a dry-bag style closure.
I prefer the MSR only because I like the coated-fabric dry-bag container.