Why does my upright freezer keep growing a snow bank behind the back panel?

A clogged drain gives you a diffrent picture than what you're describing. When the drain plugs up, the meltwater backs up and refreezes into a solid sheet of ice on the floor of the freezer, or piles up around the drain trough itself. What you've got, frost building evenly across the back wall until the shelves are choked off over a couple months, is the defrost cycle never running at all. So I'd put the drain idea mostly to rest, though flushing it with hot water while you're in there doesn't hurt since the gunk you felt with the hanger will bite you eventually anyway.

Since the heater and the clipped-on sensor are new, what's left is the path between them and the brain: the inline thermal fuse in the harness, and the board or timer itself. That little fuse is a common killer and it's a few bucks, not a hundred. It's a small two-wire part spliced into the wires feeding the heater, and when it opens the heater never gets power no matter how good the new parts are. With the freezer unplugged, you can unplug the heater connector and check those wires with a multimeter. If it beeps end to end, the fuse and wiring are fine and the board is your suspect. If it doesn't beep, there's your culprit.

And yes, the board can fail exactly the way you're seeing. They just stop calling for defrost while everything else runs normally. But don't order one on a hunch. Lots of these boards have a forced-defrost or service test mode you can trigger, or if there's a mechanical timer, a knob you can turn until it clicks into defrost. Then you can actually watch whether the heater warms up. Ten minutes of that tells you more than a hundred dollars of parts guessing. One other thing worth a glance: run your hand around the door gasket. A soft spot or gap there piles frost on fast, but that usually shows up in weeks, not months, and it hits the door side hardest.

Same experiance here with the multimeter test. My chest-to-upright swap years ago had a bad defrost circuit and the fuse checked out fine, but the heater connector itself had scorched pins inside the plug. Looked fine until I unplugged it and saw the plastic was melted around one terminal. So check the connector too, not just the wires. Cleaning those pins up with some fine sandpaper and squeezing the terminal slightly tighter fixed mine for good.

On mine it turned out to be the timer motor itself. The timer would click into defrost position when I turned it by hand and the heater fired right up, but the little motor that advances it had gotten weak and would stall out partway through, so it sat in cool mode most of the time. Freezer did the exact slow frost buildup you're describing. I found a used timer off a similar model for cheap and that was the end of it. So if your test mode makes the heater run, don't assume the board is bad, check whether the thing actually advances on its own over a day or two.

Update: got it fixed. Went with the timer idea from the second reply and pulled mine apart to test it. Turned it by hand and the heater came on fine, but the motor was dead, same as yours. Popped a new one in and the back wall has stayed clear for a month now. Cheapest part of the whole saga, of course.