I think the hammer is appropriate. This is a quasi-medieval society, so most social institutions would be quasi-religious, like European guilds and public admin would use Christian iconography. I see Inventors like masons, mixing a literal craft (masonry) with Christian-like mysticism & iconography.
This is just my own vision for them. More generally speaking, I think about FM-based world building like comic strips, where different authors can have quite different visions for their world with different ideas about key characters and groups, as long as it's paying homage to some of the canon pieces (like Batman's or Superman's origin story shouldn't change, even if you play it very differently). So I think even inconsistent visions can co-exist for something like the Inventors. They're kind of designed to be shadowy and unclear anyway, so ripe for different visions.
All that said, I think you'll get less complaints & greater appreciation if you use something other than a hammer, but still vaguely in the neighborhood, like masons themselves didn't use direct Christian iconography, but they used religious-like iconography.
Interesting. When I made the 'sun gear' banner I linked earlier, it was for my take on Mechanist-ish themes, for an esoteric group that tried to be not just inventors but heralds of Progress and the New Dawn and all that. Instead of being a religious offshoot with a messiah figure, they were to be more about supplanting the old superstitions with Reason, with the universe as a grand Machine, and Man at its centre having learnt to manipulate it; they were to be religious in the sense that Comte's Religion of Humanity was religious. Their public face was to be more of an industrialist group, so the 'sun gear' logo was ostensibly honouring the current religion, the better to supplant it later as it naturally withered and died.
(Incidentally, if anyone here with a Latin education knows about the semantics of 'futura', I've been trying to find out whether 'Ex malleo machina; ex machina futura' plausibly means what I want it to mean: 'From the hammer, the machine; from the machine, the future'.)
Of course, the very idea of a guild for inventors owes something to the glorious historical schizo-mishmash of the setting; what actual gentlemen scientists came up with was the Royal Society. I just looked up their arms and they're nothing like the stuff we're discussing here: a silver shield with England's three lions in one quarter, and more elaborate surrounding paraphernalia including two hounds as supporters.
On the hammer question, when it comes to real-world religious iconography there are lots of different heraldic crosses, some more strongly Christian-looking than others, and of course you're right, it's a natural thing for a pious armiger to want included; I wonder whether it helps that we're so used to seeing the abstract geometric design of the Cross, and we don't actually see crucifixions in daily life as we do hammers.