Tordon moves in the soil more than glyphosate. You talking about spraying green sprouts from cut off stumps or treating the stumps directly?
My first choice for cut stumps is Garlon 4, but it is harder to come by. For foliar treatment, I'd use glyphosate or Garlon 4 (If you want something hotter than Garlon 4, I just learned today that Dow has a new alternative to Garlon 3A...Vastlan. This has a "warning" instead of a "danger" on the label and only causes temporary eye damage instead of permanent. Also supposed to volatilize less). Either way, you are going to get MUCH better punch treating after full leaf out - and even more so a couple of weeks before leaf drop in the fall. I recommend Honeysuckle control be a regularly scheduled early November activity. Since you said a cross country course goes through, maybe just plan to foliar spray on a warm sunny day after the CC season is over. 3 reasons I recommend this timing:
1) It stands out very well because nothing else is green.
2) Makes it difficult to overspray onto other desirable species when they don't have leaves.
3) The plants are pulling all of the sugar into the roots for winter storage.
