You're a lot more alert than most! To minimize the risk of it jamming (which happens), best, even if it's awkward, that you go first with the stroller trailing, even if it's higher than you, so if it does start to jam (God forbid) at least you can pull it out of wedging, rather than try to push it out, which will only exacerbate the proclivity to jamming. My heart is pounding just at the thought of it going wrong.
Addendum: I just Googled to see what's on-line on this, and fortunately, there's a lot. First hit: (I disagree with putting the stroller in front, trail it)
View attachment 169526
Taking a
stroller on an
escalator can be risky. In fact, many
escalators ban the use of any wheeled device on the
escalator, such as
strollers. Nonetheless, if you do not have another option, you can use the tips in this article to take your
stroller on the
escalators more safely.
3 Ways to Take a Stroller on an Escalator - wikiHow
https://www.wikihow.com/Take-a-Stroller-on-an-Escalator
I would add that the person stand slightly sideways to be able to view what's upcoming as well as what's trailing. I learned this the hard way generations ago taking a bike down one of the very narrow escalators the TTC used to have (still has at some of the old Yonge stations?) with the front wheel dangling loose as I'd lifted it. The tire just barely touched the side-panel and being a quality headset adjusted for the lightest of castor, bam! It took less than a fraction of a second to jam and bend the wheel. Total write-off save for the hub and tube. Even the tire bead was torn. My sixth-sense still rings to this day. Far better a bike wheel than an occupied stroller!
Ditto when crossing streetcar tracks or any ruts in the road. Pull the stroller across as a trailer, rather than push.
And for those of you with dogs...if the dog is too big to lift, use the stairs, or if you're on an escalator already and realize the mistake, even a dog too heavy to lift, make them jump off the top over the comb piece which can catch their claws. I've seen that happen...it can rip the claws right off. Even slatted steel steps (think fires escapes) can and do.