Thank you for the quick reply!
Switching to quads cleaned up the additional vertices, but for some reason the segments where the Hanger is present still don't weld.
The experiments I had made:
1. I had tried moving the Hanger part so it is completely out of the volume of the Rail part to avoid all intersections of the borders, but still no luck.
2. Changes to the Generator Rules - Default, Corner, Evenly - no effect on the welding problem.
3. After I convert everything to Poly the borders vertices weld without a problem.
4. If I turn off the Hanger in RC, everything welds properly.