One thing that worries me is the response "we can only see/book the same as on website".
We already know website cannot book many fares and routes, it would be a disaster if CC is now limited to this.
My guess is that they have been instructed to tell people this, in order to steer people over to selfservice. It might be that they are understaffed and thus rather have people book themselves and loose the revenue from booking fee. But if they really are limited to the website, then this is nothing short of a disaster.
As for booking tickets, if call center can't or won't, many TA and OTA can book the fares that Finnair themselves can't. Expedia is one of them and even when using them as OTA, no need to worry about stuff as they only act as middle-man. Ticket comes from Finnair and you can manage your booking from Finnair once issued.
Generally, one should avoid OTA for tickets, but when fare can't be booked with Finnair it can't...