Re: A few things
I do a longer road trip to dodge crazy summer airfares and ship some accumulated dross from the attic to my summer house 1600 miles away on an annual basis.
Rule no 1. Avoid France.
Rule no 2. If in doubt see rule No 1.
France is by far the worst country in Europe to travel through. Idiotic junction layout, nobody following rules, horrid tolled motorways, farmers and ferry workers burning barricades of tires across the road, migrants trying to unbolt your tailgate and get in even when you are moving, you name it.
Rule 3. Plan your trip from jacuzzi to jacuzzi.
I would have expected a person who lives in the country where Carlovy Vary and Teplice are located to have groked that one out.
Rule 4. Never drive more than 8h a day except on the last lap.
The winning formula is: "less than 8h drive, dad in the jacuzzi, kids on the water slide". There are plenty of spas in Europe and _ANY_ route can be altered slightly to follow the winning formula.
In any case, the original "tax dodge math" is wrong. The legal side of things is:
1. You can have a car from a foreign country locally for 6 months. This is now enforced. The car toll and viniette enforcement cameras in all Eu countries now have a secondary feed and cars that are in for more than 6 months without re-registration show up on police database.
2. You cannot realistically have it for more than 3. The insurance treaty says 3 months, not 6 and nobody will give you an insurance for 6 months abroad unless your car is a commercial (f.e. truck). So after the 3rd month you are uninsured and can be pulled over and your car impounded. The workaround is to get the temporary insurance used in the import process locally. This may sometimes cover you for an additional month, but pulling that to full 6 months is a very tall order. It is also a royal PITA (I have imported a car into a country with penile extender restrictions similar to Portugal so I know that first hand).