If you've got Shimano gears, the easiest way to remember is bigger lever = bigger cog.
I have, but it falls down a bit as the brifters are subtly different between the three bikes.
Old Reliable (my 12 year old Apollo TDF) has Sora brifters which have a little thumb clicker on the hood to change up, and you push the whole brake lever inward to change down.
My B'Twin has a bigger, downward-pointing clicker to change up, which I click with my forefinger; again, to change down, push the brake lever inward.
The Cube is a paddle within a lever, as you describe.
When I bought the Cube, I was forever changing up on steep hills inadvertently as I was so used to the B'Twin. I have the hang of it now. I think.
Speaking of big guys looking to improve their climbing, as the OP was; whatever became of
@blazed, "the world's greatest 200lb + climber" (sic.)? He used to make me smile. A lot.