If we promise alchemical reagents (effectively a form of magic that doesn't require innate talent to use; something I'm sure men of science would find interesting) to some of the more corruptible Singularity archaeologists (the ones with little loyalty to the nation they belong to), we could bribe them to argue against the protesting archaeologists and insist that no technology is used in the Floating City. After all, their nation are experts on technology, so they'd know if something was built with it.
I dunno, they're archaeologists, not alchemists. They'd probably be more interested in some ancient artifacts.
Convincing archaeologists is the way to go, but I think we'd be better off doing something like
Sponsor an Archaeological Conference: We host a grand event in the floating city, which archaeologists from far and wide are invited to attend. Many topics will be discussed here, but with the aid of Charisma Powder, it shall be our archaeologists who manage to convince the (unaligned) majority that whilst, yes, there is
some technology involved in the floating city's flight, said technology is primitive, and really much less important than the magical aspect.
Once the majority agrees with us, the Singularist archaeologists will have a much harder time making their voices heard. And surely Singularist constituents believe in the scientific consensus?
(Please let me know if this is too ambitious for a revision. My thinking is that it is basically just a fancier way of presenting the propaganda developed in the design phase, targeted at a specific group)