The comment you replied to is correct based on what you said - if you start in a state in permanent summer time, travel south to a state in permanent winter time, keep travelling south to a state in permanent summer time, and so on, you will be going back and forth by an hour repeatedly.
Hypothetically, if you start just north of Sittard and east of the German/Netherlands border (in Germany), and travel in a straight line, almost due south to Geneva in Switzerland, you could, depending on what time member states choose to permanently adopt, potentially go from German summertime, to Dutch wintertime, to Belgian summertime, to Luxembourgish wintertime, to French summertime, to Swiss wintertime, all in under 350 miles and with not much deviation in longitude.
Hypothetically, if you start just north of Sittard and east of the German/Netherlands border (in Germany), and travel in a straight line, almost due south to Geneva in Switzerland, you could, depending on what time member states choose to permanently adopt, potentially go from German summertime, to Dutch wintertime, to Belgian summertime, to Luxembourgish wintertime, to French summertime, to Swiss wintertime, all in under 350 miles and with not much deviation in longitude.