This is an interesting proposal. Technology versus magic is a great theme; this could be an opportunity to explore creativity among players.
As I understand your proposal so far, Ingineers basically use alternate types of card, with technology themes rather than magical ones. Presumably, ingineering schools would be mutually exclusive with magic schools so that cards from one cannot be used in the other.
But even with alternate schools (and please correct me if I am misinterpreting your proposal), Ingineers use basically the same mechanics as mages, in terms of playing cards from preconstructed spellbooks (toolboxes? workshops?) to accomplish their goals. What if this was used as an opportunity to explore a different but compatible mode of play?
Lately, I have been working on modular spells, and the idea of a nonmagical tinkerer (the association that the word "ingineer" brings to mind is a sort of eccentric inventor/scientist type) would be a perfect thematic opportunity to design a character that fights using ingredients that are put together in novel combinations rather than precomposed objects.
What do I mean by this? Let's take your proposed school of Composition, specifically the part related to chemicals. You could represent these with "potion" cards that have specific effects. Each potion is unique, and distinct from other potions.
Alternatively, you could have "ingredient" cards which may be combined to create an object with an effect determined by the cards that comprise it. I think you might be getting at this; you mention:
Items used by Ingeniers trained in composition include containers with chemicals in them, a variety of tools and gadgets for taking things apart and putting them back together, sometimes including things like hammers and screwdrivers. They can sometimes even steal materials from their enemies to build new items.
But rather than thematic scavenging and recombining of resources, what if the entire play of an ingeneer was based on putting things together? You could build steampunk machines out of mechanical parts, create potions out of ingredients, and breed weird abominations to fight for you. Each object that you brought into play could be comprised of several ingredients from your toolbox; you could even create recipes/blueprints with your ingredients and then field multiple copies with a generic placeholder card.
Basically, I am suggestion that this "Ingineering" concept adopt modular card mechanics to further distinguish it from the magical style of dueling. Without incantations, attack spells, or enchantments (though traps might play a role), the focus would be on creativity over tactics (obviously tactics would still have a place, though). It seems to me like it would fit the spirit of what you are trying to accomplish.