I've got a Brother HL-L8360CDW that I got last year, and it keeps jamming whenever I try to print from the bottom tray. The top tray works fine. I've cleaned the rollers and checked for bits of paper, but it still does it.
The tray height thing is real, but I'd also check if the pickup roller on that bottom tray is worn out or glazed over - happened to my printer and it was just not grabbing the paper properly anymore. Try giving it a good clean with a slightly damp cloth or some isopropyl alcohol, sometimes dust and toner buildup can make it slippery. If that doesn't work you might need to order a replacement pickup roller assembly, they're pretty cheap and not too hard to swap out yourself. One more thing - make sure you're not overfilling that bottom tray, I used to cram too much paper in there thinking it'd be fine but it actually made the feed mechanism work harder.
I'd check if the bottom tray is maybe sitting slightly too high or if the paper guides aren't adjusted snug enough to the stack - mine did that and it was driving me crazy till I realized the tray wasn't seated all the way in. Also worth trying a different type/brand of paper to see if it's just not feeding that particular stock well.
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