Selina,
It's really not as bleak as it sounds...
Under the federal law (as it stands today), your dogs you are not subject to the mandatory training classes, as they will already have been registered to you when you import them. So that's one less worry.
You would have to take the practical course with any dog you acquire after moving to Switzerland though.
It's recommended to get involved in a training club or take a few classes, however, as it's a good way to learn what Swiss society expects of dog owners. It's also a great way to make new friends.
Dalmations and Weimeraners are not on the Basel BSL list, so that's one more thing you don't have to worry about.
You won't have general on-lead restrictions in Basel, except those that apply to all dogs: wherever so signed, during night time quiet hours, in woods during hunting season and in the spring, in nature conservancy areas, cemeteries, schools, etc. You can bring the dogs down to the pub with your or into restaurants as long as they are on lead.
The laws in Basel Land are here:
http://www.tierimrecht.org/de/tiersc...basel-land.php
And Basel Stadt:
http://www.tierimrecht.org/de/tiersc...asel-stadt.php
In Basel Stadt, you will need a permit to keep more than 2 dogs. That could be a problem for you.
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You will need to pay the dog tax every year - I believe it is around CHF 150-ish per dog. Check with your Gemeinde for up to date info.
You will also need to have private liability insurance, usually a cover of ca 3 million, which costs somewhere around CHF 50-100, usually regardless of how many dogs you have.
Your dogs may indeed run off lead in public places in Basel (only SZ has general on-lead restrictions) where there are no signs indicating otherwise.
Your dogs must be under control and in sight at all times. 'Under control' can also mean under voice command if your dogs are trained to a reliable and immediate recall.
You must pick up after the dogs.
It sounds like you are a very responsible dog owner, and already do these things.
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Yes, having multiple dogs is indeed expensive. Housing should be your first concern - a single family home with garden really is a necessity with 6 dogs - and you may need to be prepared to pay a bit more to find something suitable.
But, as I keep reminding my husband, having a herd of dogs is really no more expensive than stocking his wine cellar, or building model trains, or dining out, or skiing... or any other hobby we might undertake.
There are several Basel area dog owners active on this forum - hopefully some will pop by soon to give a better idea of the day-to-day reality of having dogs in Basel.
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My take - bring the dogs. They will enrich your life here in so many ways. I've lived in some places which at first glance would appear to be dog-unfriendly (for instance, Beijing in the 90s), and have always managed to give my dogs an excellent quality of life. With a little common sense and a little creativity, there is always a way.
ETA:
Check with BVet - I think there is a restriction about importing more than 5 dogs at a time as a private person... If so, do you have a partner? If so, each of you should import 3.

Otherwise, bring them over in two separate trips.
ETA 2:
As you are weighing your options, if you decided you could not bring your dogs, what alternatives are there for them? This should be the primary concern. One thing I know from moving my dogs around the world a few times - while space and amenities are a big plus, more than anything else the dogs want to be with us. The bond they share with us is the thing that contributes most to their quality of life, not the size of our gardens. (Hmm - that sounds horribly egoistic, but fellow dog lovers will understand what I mean.

) You will find places for the dogs to run, it just may take some organizing. But that's Switzerland - organized.
Wishing you and your dogs all the very best.