Looking on EF, if you ask it for BUD-HKG, via HEL on AY, there is no L inventory (not L0, but no L inventory class). However, if you ask it for BUD-HEL and HEL-HKG separately, there is L inventory. I don't know why it does that. In the online tool, can you not simply pick the two flights separately? There are two flights BUD-HEL (11.40am/3.00pm and 7.15pm/10.35 pm); the later flight connects to the 11.40 pm flight to HKG). Does the earlier flight result in a stopover (even though it's a less-than-24-hours connection)? Setting up a dummy itinerary in the online tool, it did not appear to have a problem selecting the flights separately. I also asked it for BUD-HKG and it gave me the AY flights as a pair (and correctly identified it as using two segments); it confirmed the inventory was available (though I may not have been using your dates). Obviously, YMMV.
I just tried it. I can select the two flights separately ie BUD-HEL and HEL-HKG then HKG-KUL; however, it adds an additional segment. I was getting to KUL: BUD-LHR-KUL (3 segments instead of 2). I'm maxed out with 16 segments already.