I love my Escalera, but it is easy to get yourself into a bad spot if you don't know the potential problems.
The handles will try to pull away from you, trying to pull you into the dolly, at varying degrees of strength depending on what stage you are in for the stair climb. It is not a constant pull, you need to adjusting the balance of the dolly.
When going up stairs the most pull is right when it starts to climb new step.
When going down stairs the most pull is right before it gets to the top of the next stair.
The worst is on steep stairways when you can't lean the cart back enough to get it to balance. The very steep Bilco style doors that go into basements are the worst, some of those can almost be as steep as a ladder.
Going down one of those steep stairways is where I got as close to being thrown over the top like the OP. I was moving an ~550 lbs cast iron furnace down into a basement. The first two steps were fine, I was still on the ground and the cart had not yet gotten almost vertical as I went down the step stairs. The problem came when the cart was going towards vertical going down the steep stairs, I just did not have the weight to keep it from tipping forward. It was not a strength issue, it was a how much weight could I push down the handles because I could not tip it back enough to balance it. Luckily I had a helper to add his weight and we made it down, but without him I would have flipped over the cart, let it go or maybe if I was lucky try to reverse direction before I totally lost control.
It is like being on a teeter totter. It is not about strength, it is a weight issue when you get onto steep stairs.