OUR UNOFFICIAL ANSWER
It sounds like the main reason for wanting to check in for the next flight
right after you land is the bulky luggage which you don't need in HK. Maybe
try check those through to your next destination rather than picking them up
But for your info, if you take the Airport Express, you can use the trolleys
all the way up to the doors of the train itself, and then when the train
arrives in the city, there're trolleys you can use at the train doors as
well to take your luggage to the taxi stand. I suppose you can take the
trolley to the city checkin counter as well.
Yet another alternative if the rest don't work: there're storage lockers and
also a place for you to store luggage for a fee. Fees for lockers for the
first 4 hrs: small and large - HK$20, jumbo - HK$30. For any 12 hrs
thereafter: small and large - HK$30, jumbo - HK$40. (See
Have a good trip!