If you are looking across Star Alliance as opposed to only SAS, I would suggest you try search via the UA website - no sign-up needed, and at least it gives a good indication as to what is available. Note however, that you cannot be 100% certain that what is available to UA is available to SK. But for what it is worth, this is the way I have found our recent many business class award tickets.

I have found the recently added EuroBonus award search for Star Alliance flights through the SAS website very unreliable, and when I finally made it show what I was looking for (found via UA), the reservation came up with an error But all was solved by a call to the EBG/D hotline.

That said, three tickets during Easter holidays might be tough at this time as availability during traditional holidays tend to be snapped up as soon as they are made available.

Hope this helps - good luck!