FYI, crystal overtones are just that -- overtones, not harmonics. They're usually a little bit above harmonic. There may be more, and stronger, spurious modes around the overtone as well (depends on cut and holder design), and the tempco will be a lot stronger (also depends on cut).
Normally, overtone crystals are cut for the purpose, to account for all of this.
If you're going to do it, please do report back how well it worked out -- if you can, try to plot the impedance and bandwidth of the overtone, and the spurs around it, and see what happens at different temperatures. I would expect a tuning-fork style crystal to have a strong overtone, but I don't know that it will be useable. Good luck!
On a related note, I have a 100kc crystal handy -- but it's not 120, and, as you might guess from the "kc", it's somewhat antique (dated 1959ish I think it was). Quite stately in its metal can. :-) Looks like a contemporary electrolytic capacitor, or octal audio transformer, but just two round pins.
Tim