Use both hands. It sounds simple, but it gave me about a 50% speed improvement over time once I got used to it. It will feel awkward at first especially if you're one of those who can't do much with their non-dominant hand. Like myself, I'm right handed and I can't even hold a pencil with my left hand unless it's a fist, but you'll get accustomed to it.
Zone block by block. Try to spend no more than 5 minutes on each 4 foot block. Fix the major issues and if you have time, come back and do what I call the "OCD Zone" making everything look especially pretty. If your store has a visit upcoming, superzone the first 4 foot section facing the racetrack of each aisle and the front endcaps, and do a regular zone of the rest. If you have time, come back and superzone the second section facing the racetrack. This makes it look, from a "walk the racetrack" perspective, like a better zone. This doesn't mean disregard the rest of the zone, it just means pay special attention to the first parts of it.
Work your strays as you find them, within a 5 aisle radius. I try to divide my cart into backstock (bottom), non-department strays (child seat), within this 5 aisle zone strays (front of big basket) and all other in-department strays (back of big basket). When I finish 5 aisles, I work the strays for those aisles.
Walk the aisle first and pull all the strays. This will make it easier to zone what's actually supposed to be there.
As hard as it can be, try to reserve the "OCD Zone" for last. First, worry about pulling at least 3 items forward and covering the diamonds, and later worry about such things like "are the boxes perfectly lined up with each other" and "is it ruler-straight with the front edge of the shelf"
I'm not sure on your store's volume, but at my store, I (photo closer) am assigned all of Movies, Music, and Books (H block) and Stationery (Half of G), but sometimes if the LOD feels vindictive, H block and Toys. I can usually finish H block and stationery in my 3 hour, 45 minute shift, but that's just a "make this presentable" zone and does not include H block re-shop (which the photo opener does) and going for backup, but it does include helping guests in electronics.