What about putting it horizontal? Put the filter on a broomstick and lay it across 2 chair backs/ladders/buckets/whatever. Like you're roasting a whole pig on a spit LOL!
The reason I clean mine vertically is so the crud rinses out. My filters have sections, and each section has a bit of a wall between it and the next section. I start with the top section and clean it all the way around before starting on the next lower section. I reach in with a nozzle and clean each pleat. The crud tends to jamb up at the bottom of each pleat, where it meets the section wall. So I have to give it an extra "shove" with the water stream. It eventually all falls out and down. If the pleat was horizontal, I expect it would be hard to clear the pleat, unless the pleat would be facing almost down. Then you'd either have to bend way over and shoot the water stream upwards, which would be very back-breaking, or raise the cartridge high enough to work on, which would then soak you completely as the spray shot out and down from the pleat. (I pretty much get soaked anyway, but I can at least shoot the stream downward and minimize the splash back.)
Working top down with the cartridge vertical tends to keep the parts I've washed clean. If I was working horizontal, I think the crud could get back into the sections already cleaned. With the cartridge horizontal, some number of pleats are always going to be facing up, trapping water and maybe collecting dirt?
I dunno. I've never tried it horizontal. Can't hurt, give it a go. I'm just predicting it won't work as well as vertical.
The broomstick on the chairs is certainly an easy thing to build, but I think you'll find the broom sliding around on the chairs as you work and turn the cartridge. A fixed stand is the way to go. You'd want to at least tie the broomstick to the chairs somehow to fix it in place. A wider pole might work better, like a length of 2" PVC or ABS.