Thanks for sharing your experience. I was trying to approach this question from a simplified physics perspective. Here are a couple of examples.
While standing up, you burn more calories than when you are sitting in a comfortable chair, even though no real work is being done. Why? Because human muscles are not conventional electric motors. Your muscles are burning calories in order to maintain your upright position. Ditto for wall-sits, which are popular with skiers.
From a physics perspective, ordinary walking consumes calories, simply because your center of mass is fighting gravity, in moving up (and down again) an inch or so every step. This is true, even if you have a mild tail wind.
Beyond that, walking 'uphill' on a treadmill does not do any extra work.
Essentially, no real work is being done when you maintain your vertical position on a treadmill, or in trying to go 'uphill' on an escalator that's going downhill at a velocity thats equal and opposite to your 'groundspeed'.
In walking 'uphill' on a treadmill, you rely more on the big quadriceps (thigh) muscles, which are doing precious little real work, but are nevertheless consuming extra calories. In level walking -- on the ground, or on a treadmill -- the gastrocnemius muscles, in your calves, are doing a bit more real work In both examples, the butt muscles play active roles.
Biology sometimes makes basic physics more complicated!