Thanks to Pedro von SimuJabs who was able to exactly replicate the Boeing 737-300 J-Rails I could now mount the original cockpit seats. Original J-Rails are very hard to get and the often replicated Boeing 737NG J-Rails are not compatible to the Boeing 737 Classic mounting holes.
At the end, I had to still move the mounting holes by 0.5-1 mm, but the seats now move freely. Like with many completed steps in the cockpit building project it is now time to remove seats again to get space in the cockpit and store them until their final mount.