Both varieties you mention are derived from vigorous scandent species from the Hiamalayas. In the wild they often reach into the upper crowns of quite tall trees from which they then drape back down again in long curtains of growth. Because of this habit, they are best trained into a suitable tree (an old apple tree is the usual quoted subject) where the sparse lower stems don't matter so much.
In your case, try leaving more of the young cane like growth which can be tied down to the horizontal for more flowers next year. Remove as much of the older flowered wood, tracing it as far back until you reach a strong young cane that will replace it.
Feed with a high potash fertilizer twice a year to encourage ripening of the cane growth and flower production. Best of luck with your two monsters!