Chemicals . . .
Amino acids could be inhibited, with a resin designed to dry up seedpods, thus rendering a tree sterile. That might be the best way. Killing the tree outright might be concidered hazardous, as we would then have to cope with needing to cut down the whole forests as soon as possible. Doubtless a boon for lumberjacks, but still quite dangerous.
As you surmised, the trees would have to be identfied and injected by hand, with followup monitoring. Time consuming and expensive, but doable. The hard part would be getting the goverment to recognize the threat, and to set up an initiative.