Well, let me (continue to try to) approach this from the Scientist/Engineer perspective.
Not so much. HAM is keyworded as Touch, and LSC doesn't modify that. They're probably worth getting anyway; even if we can't get sorcerous training to all of Japan, every extra sorcerer helps. Also, it significantly reduces training time for almost everything else, including our first dots in Craft (foo).
The prerequisite for both of these charms is Lore 5, but that last dot may not need to be bought with a quick-learn slot! Lore is favored for Amu, so she should be able to buy it "immediately" with pure XP. (About an hour, if I recall correctly.
@Baughn?) Lore 5 is also the prerequisite for Wyld-Shaping Technique and Wyld-Cauldron Technology, which should help significantly in making things out of magatsuhi. Once we understand m-physics well enough, at any rate.
Lore 5 is also the prerequisite for Immanent Solar Glory, which would allow Amu to regain Essence by "tending to the affairs of a kingdom, organization, or military group which [she] leads."
A dot or two of Occult would be helpful as well, but unless Amu's going to be going into Sorcery (and I do
not recommend this) there are no really useful Occult charms.
Craft, on the other hand, is
not one of Amu's favored abilities; we'd have to either spend quick-learn slots on it or use HAM+LSC to learn any reasonable amount in less than a season. The likely-most-useful Craft charms are Chaos-Resistance Preparation (Craft 4; strengthen an object against the Wyld), Crack-Mending Technique (Craft 5; quickly repair even irreparably damaged objects), and Craftsman Needs No Tools (Craft 4; obviate need for tools
and speed up all Craft work by a factor of Ess x 3).