You are a bit more intensive with your inquiry than I am prepared for. Quite frankly, I have never seen morning glory vines that were difficult to control; I suspect that the perennial vines don't like it around here. I've seen the annual vines, but never woody nor very problematic.
My initial internet search prior to giving my answer suggested that "morning glory" vines may be of several completely different species, depending on whom you are talking to. Wikipedia says there are over 1000 specie, so I think what we get around here are not so vigorous. Wikipedia also suggests that they are not very cold tolerant perennials, so that may account for my observations.
I get pretty good results for almost everything with Barricade (prodiamine) or Dimension (dithiopyr), but these are principally turf herbicides that don't attempt to list pre-emergent control of woody plants.
We do get the field bindweed around here, but it is non-woody, and we get rid of it with broadleaf weed control. It usually doesn't persist in competition with trees, and it is quite the pest growing over shrubs. Non-woody, our variety is easy to hand weed. Barricade seems to keep this out of the shrub beds.
Obviously, Velpar would come close to killing anything in its path.
I use quite a bit of Tordon (22k! I mix my own -RTU), and have never seen injury to adjacent plants from careful stump treatments. The problem is that most operators don't trust the herbicide, and apply too much. Tordon is much slower to affect the plants than normal broadleaf herbicides, and this inclines some folks to put on too much also.
Get a sponge, dip it in some -RTU, then daub each cut stump (freshly cut, while actively growing) until it is blue from the marker dye. Dead !