I'm always the slow learner, and my questions can show it.
SO, are you talking about using a head tube reamer to shave off a bit more than the usual facing job? Instead of 6mm, try 2-3mm. If that's all you mean by "cutting the frame", then that should be fine.
That CLB hanger is monster thick. It could lose 1-2 mm without any problem.
Do match up the washers, tho.
You also haven't mentioned the condition of the headset bearing faces. The Stronglight P3 can be found in NOS for, usually for reasonable price. Everyone wants the S4 or fancier ones. That bottom cup is also rather fat, and I'm not sure it's a Stronglight, although the top looks vaguely Stronglight-ish (maybe just French generic?).
Check the GitaneUSA site, as it is full of French thread fans and spare headset parts probably easier to ask for there. Again, search for Vertkyg's posts, too.
Handing blindly over to your LBS says, either, you know the mechanic well and trust him..., or you're crazy.
Sweet looking bike, either way!