Hello, hopefully someone learned can help me with this scheudle - what's the best way of booking / pricing this up?

Looking to go FRA - BKK on Finnair via HKG, coming back from BKK via HKG but on Cathay Pacific direct to FRA. All in J
On the Finnair website I can book the outbound combination as follows:
Sunday 22nd December:
AY1412 FRA - HEL 11.35 - 15.20
AY101 HEL - HKG 16.55 - 08.40 (Mon)
AY5115 HKG - BKK 13.05 - 15.10 (operated by CX)
I quite like the look of that combination as it gives me a chance to try the Finnair A350.

Coming back I would prefer to connect from BKK to the direct Cathay Pacific flight from HKG to FRA rather than going Finnair via Helsinki, but Finnair obviously won't allow that option as all their legs go via Helsinki. The Cathay website will only show CX flights. Ideally I would like the following combination coming back (this flight is offered on the CX website - I am looking for a day in Hong Kong):
Friday, 17th of January:
CX700 BKK - HKG 08.25 - 12.10
Saturday, 18th of January:
CX 280 HKG - FRA 00.35 - 06.10

I have tried pricing this up in Google flights, but that only shows the Finnair flights - do I need to go through a travel agent to book this or can this somehow be done online? For context, the Finnair flight is around € 2,600 if I choose straight FRA/HEL/BKK and the CX flight is around € 2,800 if I go straight FRA/HKG/BKK.

My apologies for somewhat long post, but I am still new to the whole connecting / different legs on different airlines thing and I am just trying to find out whether I can book this online. Also, just for my personal reassurance, I can still all credit these to my BAEC account (mainly worried about tier points), right?

Thanks very much!