It’s been a few years now since we traveled with our daughter’s stroller, but the Prampack sounds like a good solution to the potential damage from mishandling. We were always happier gate checking her stroller than we were with checking it with our bags, but we were never completely sure it would be ok (fortunately, we were lucky and never had an issue).

It sounds like you’ve got it sorted out; sorry I couldn’t be of more help.