Just so you can find what your looking for better, it's not referred to as "Shutzhund" anymore, depending on the club it's either IPO or IPG
If you really like the dog sports with bite work then also look into PSA (Protection Sport Association) and French Ringsport.
French Ring is really tailor made for the Malinois and PSA is a more modern dog sport that puts lots of emphasis on dealing with distractions (ie: having your dog ignore the decoys in the bite suits while you have the dog heel). I think only a handful of dogs in the world have ever actually earned PSA level 3
The new name of the sport is IGP. But many local training clubs will have Schutzhund or IPO in their club name because IGP is only been called as such since 2019.
French Ring isn't tailor made to the Malinois, but Malinois excel at it. There was a time where Ring was dominated by GSDs and Dobes in France. An era bygone now. PSA is also mostly dominated by Mals and Dutch Shepherds. There is no PSA3 Doberman in the history of the sport, it is much much more than a notion of focusing with distractions, it's a sport that combines elements of all other existing protection sports and will put the dog under extreme pressure. It's not just about the distractions it's also about the level of adversity they will face, and the fact your dog has to be genuinely trained to expect the unexpected since PSA3 always includes new surprise scenarios that have never been done before. You are correct that the "PSA3 Club" is very small. What makes it distinctive from other protection sports aside from the obvious is that there are huge leaps and steep learning curves between the PDC, the PSA1, PSA2 and PSA3.
PSA got that wild unpredictable factor from Mondio Ring which is also a lot of fun, similar to French Ring but a bit less difficult on the actual bitework (decoy's in French Ring must do everything in their power to make the dog miss the bite, and at the highest level can even attempt to block the dog. In Mondio they cannot block the dog.), more difficult because of the unpredictable nature of the items on the field and themes.
The only other sport that has the same level of intensity as PSA imo is Campagne, which is exclusively French. It can include scenarios on a lake or a river where the decoy tries to flee on water and the dog has to catch up to them. There are also a couple of clubs in the US attempting KNPV but the Dutch don't actually want to export it, so it is 'unofficial'. Belgian Ring is also a thing but I don't think it is practiced in North America at all, and I don't know anything about that one.
I think IGP is the only sport that includes tracking, though some of the others can have a scent/search component as part of the OB and/or protection.
Ahem, back to OP: the look of european dobermans you like will be less common in actual working lines. European show lines will vary in temperament and drive same as Am lines, (and there are a lot of shitty nerves coming out of certain east european countries in particular) so do your due diligence. The UDC is probably a better ressource to get a dog with the look you want but still maintaining the grip and temperament you need for IGP, than attempting to import. There are lots of very nice working, european dobermans in the US and Canada now.
There's also an increasing amount of breeders mixing American and European lines together to attempt creating well balanced all around dogs and hoping they will be healthier.