First things first: the paint can hack I tried worked so well that I want everyone to know about it:
You can buy pour spouts for regular-sized paint buckets, but a) this is a two-gallon, not a one-gallon bucket, b) I am only sometimes, not always, not pathologically frugal, and c) most importantly, I feel like this probably works better than a rigid pour spout would.
I thought, when I first saw it, that this hack was merely about narrowing the opening the paint poured through, so that it wouldn't spill so badly. And I'm not saying that doesn't help. But if you carefully observe where the tape meets at a point in front of the bucket, you can see it forms a weird almost-triangle for the paint to pour over. If you lay that tape-triangle across whatever you're pouring the paint in to, the paint flows right across it and you can even wipe it off with a brush if you want and it works so well that it's fun and makes you wish that the entire job consisted of paint-pouring.
So. Now you know about the exactly one part of the fence-painting process that has gone smoothly.
I'm not even going to try to tell you what I did in order, because it was such a disorganized mess that I can't remember. What I can give a little more coherent an account of is what I should have done.
Part of the problem is that my problem is so unusual: after all, who paints a half-rotted fence in high-gloss paint, waits five (or more-- not even sure) years, and then repaints it? I mean, me, obviously, at least for the repainting part, but while I would normally try to do some research into the best way to attack house-repair problems, this one was so weird that I didn't feel like that was a viable option.
(I keep wondering if it's even worth it, since I'm pretty sure that the fence is going to need to be entirely rebuilt in 5-10 years, but I WAY don't have it in me to rebuild it this year, and the paint color, barn orange, does stand out for weirdness/ugliness in the neighborhood.)
But, as I said, this is what I should have done. First, remember that you don't want to paint anything that is too rotted, so figure out some sort of scraping system that pulls off the most egregious stuff before you start. This maybe should have been obvious to me, but you will want to remove the largest debris first, and then work your way down to the smaller stuff. Here are some tools that will be helpful:
A Phillips-head screwdriver; a wire brush (which are evidently a terrible idea to use on grills, but since you aren't planning on cooking anything on this fence, let alone eating anything that has been cooked on it, you're good to go); and a plastic scrub brush you originally bought because the level of pollen on your front mat was deep and concerning, and you hadn't figured out yet that this is why power washers were invented (and borrowable from the library).
Use the screwdriver to scrape away the vines that the last painting crew didn't bother to take care of, which are now rotting under the paint. Then, take that wire brush and scrape off what was left by the screwdriver. The plastic brush takes care of even smaller debris, and then after that it's time to power wash.
Which, it turns out, is VERY fun. I have a friend who works for the Foreign Service, and before she went to one assignment in a high-conflict area, her training included learning how to use a machine gun. She said it was by far the most fun she had ever, ever had at a work training. I thought about her as I felt the kickback from the power washer and noticed that, while it's tiring, power washing is indeed also quite fun.
I have no current plans to get a job that requires me to learn how to use a machine gun, but I did what I could to live up using the power washer while I had it.
BTW, past self, please do yourself a favor, suck it up, and commit to moving the ladder around so that you can power wash the fence from the top down (instead of the side, as you keep trying to do), because that will be much more effective.
Also, don't even bother with the power sander. This high-gloss-paint-on-weathered-wood situation means that the power sander can't really reach most of the paint. You will eventually notice, in fact, that the sander is called a "finishing sander," and the painting situation you are in calls for beginning sanding if there ever was such a thing.
Fine-grit sandpaper is maybe 200-400 grit. Medium sandpaper is 100-150 grit. Coarse is 60 grit. You will briefly consider driving an extra 20 miles to get 36-grit sandpaper, but listen to me, you could skip all that and go straight to buying the not-to-be-used-on-a-grill metal bristle brush. After you've used it to get the debris off, as I described above, you can use it to rough up the entire high-gloss surface of each board in preparation for priming it.
And, as is so often the case, I'm too tired to write any more tonight! Next week-- er, in two weeks-- I'll see how much further I can get in the Saga Of The Not Yet Painted Fence.