Re taipeiflyer
You are not 100% in the right because buggy is not an entitlement and you should have left enough time to hoff it over to your HKG-TPE gate on foot.
But other than that I am sypathetic with your case - especially since CX lounges have form in this regard (my own experience included)
http://www.flyertalk.com/forum/catha...ded-4-oct.html