As someone who's been risking his sanity playing mod support on this forum for ~2 years ... I really don't need to be told that most people are chronically lazy.
Which is no excuse. You want install something for yourself, you read the instructions. Of course the fact that the OP does not explicitly mention Mantle has to be installed along with TiCon (it only semi-vaguely implies with the fact there are 2 download links) does not help.
As I explained above, it wasn't an issue of laziness, it was one of familiarity. I've used Tinkers before, and when it was in Hexxit it did not require Mantle, so I assumed that it relied only on Forge as before. If it was a mod I had never used before, I'd have checked more carefully.
In either case, the issue is solved, so thank you folks for helping me to fix it! It's a great mod, and in particular I've always really liked the self-repair weapon modification, which I feel works at just the perfect rate to be worthwhile without being overpowered. Way to go to the mod authors!
I see both bows and throwing weapons have changed substantially since the last Hexxit release, so I can't wait to try!