If you search this forum you will find a number of FTers (including me) with bad GOT experiences. It might just be the worst SK station. I know for sure HONs are treated properly at ARN (Stockholm) with HON tags available at CI etc.
As a general observation there exists a number of problems in the communication between SK and LH checkin systems. One result is that you can not OLCI for LH flights ex Scandinavia. Also SK agents typically doesn´t have a clue about seat blocking (SK doesn´t have that feature) and I honestly think SK agents can not technically do it for LH flights even if they would like to due to technical limitations.
Why your HON status is not recognized as *G is beyond me.
If you have the time I suggest you write both SK Customer Relations (as they acted handling agent, lounge operator etc) and HON member service about it.