Simple fix would be to simply have a vertical and horizontal version of the block tied to a mleader style. Then simply change the desired mleader style.
Why is the drawing getting rotated? It seems that the "correct" way to do this is DVIEW TWIST ?
Maybe post a drawing with before and after results.
Some searching yield something that kind of works
https://forums.autodesk.com/t5/visual-lisp-autolisp-and-general/block-mleader-rotate-an-existing-mleader/m-p/7665762/highlight/true#M363381
If this is always an issue, is there a possibility to change your leaders to have mtext content? Then this would be VERY easy :).
Well it was worth a try :) . Seems like recreating the mleader would be the easiest for this then, but you'd still have some manual cleanup.