Thanks man! I saw you live in Sweden and had to chuckle. I have this romanticized notion that ASSA Twins, Combis, Pros, and all the other best locks in the world are just falling from the sky in that area. It's a little sad that they can be as hard to come by there as they are here. I really love ASSA locks, and am always keeping an eye out for them, but they are very uncommon and tend to go for a lot of money when they do show up for sale.
It's cool that you have a Combi, but a bummer there is no key for it. I guess shimming the drivers is probably a good idea, and you can isolate the sidebar that way. I found with picking the sidebar that the best method is to lift the pin a little. Sometimes you'll feel a little set, but often you wont. Once you've lifted it a bit, release much of your tension and try pushing or pulling on it. When it finds its true gate, you'll get a distinctive click and a bit of core movement. You'll have to push or pull pretty hard on them along with pretty light tension to get them to move. They really like to settle into those teeth on the sidebar.
Primus is a really fun lock to pick and I found that it was a great way to get prepared for the Combi. The pins rotate much easier, but the distinctive feel of them setting is very much the same. I share the same concerns as you. I only have a handful of ASSA locks. I can pick the ones that I have, but don't really have much confidence in my ability to generalize the skill. If Primus cores are easier for you to get, it does seem like a good idea to work on those. Please do let me know how it's going with the picking. I'm happy to try to help in anyway I can with the little bit of experience that I have.