I did something similar just a week or two ago, but in the opposite direction...CX 565 KIX-TPE on one ticket connecting to CX 565 TPE-HKG on another ticket, first ticket in U class while the second one in I class (i.e. both business class).

At check-in at KIX - the agent was able to give me boarding passes for both segments. But for lugguge, she claimed that she was not able to do it for me - I could not check it through to HKG, instead I had to claim it in TPE and then checked it in there again (which is quite a challenge for me in terms of timing because I need to get landing visa, then go through immigration, wait for luggage, go through customs, then go to departure floor and check in, going through immigration and security - too tight for a one-hour connection I think).

I don't think it's right, but she claimed that she has checked with her supervisor and everyone there already and there's nothing else she could do. What I think is - yes, she could not tag it direct KIX-HKG (because I had 2 tickets), but she could tag it KIX-TPE and then TPE-HKG, although both are CX 565...since the connection time in this case is still more than the minimum connection time - i.e. in TPE they probably need to unload it first, but then just need to load it again on to the same flight.

She said, if I am taking another TPE-HKG flight, then she could check it through to HKG, but not the case if I am doing KIX-TPE and TPE-HKG on the same flight number.

Anyway, she didn't agree with me and there's nothing I could do to convince her. And I could not afford to wait another hour in TPE for the next flight that day because my time was very tight in HKG. She instead suggested me to take the lugguage on to the plane (I don't know the exact dimensions, but me personally have never seen people carry luggage as big as this on to the plane) - I was a bit surprised as I never thought I could take luggage this big on to the plane, but she said I was traveling business class anyway and it isn't a problem. And that's eventually what I did.

While on the way to TPE...the FA/ISM asked me whether I was getting off in TPE or HKG, I said HKG - but they said according to their record I was going to TPE only. Then I told them about my separate tickets and gave them my second boarding pass for TPE-HKG, and they at TPE gave it to the ground staff, gave me back the small piece, and let me stay on board the plane for the hour they were doing cleaning etc (like others doing the one-ticket KIX-TPE-HKG flight) - but I also could get off the plane to stretch a bit if I wanted to, according to them.

But frankly I think it's quite a hassle carrying the big luggage on board and for my future reference I'd really like to know if the KIX agent was right (esp in my case where the TPE connection is more than the minimum connection time - so why couldn't she treat it like 2 flights).

Hope this helps...and hope you have better luck than me checking your luggage through.