Working in IT and having helped with certain similar projects, I can say that the lions share of that budget NASA made for a metric conversion isn't for the actual conversion.
It's for the verification.
And now that I'm peripheraly involved with defense/aerospace Quality Assurance, I'll wager that with manned spaceflight, and with multi-million.. billion dollar probes that are launched on one way missions forever out of reach of any repair, that they can't just do a statistical sample of all the documentation and code to "verify" things.
They'll have to go through every piece of data they have line by line. And it's not just simply going though and saying "Okay, 1 inch equals 25.4 millimeters...", they'll need to figure out significant digits, and acceptable tolerances for each conversion, for some things like laying out the roadway for the crawler-transporter, it won't matter. For others like a space probe trajectory to an outer planet where a difference of .00000001 of whatever unit will stack up every second like "compound interest", that can be a problem.
And then they'll need to test some of those conversions in simulations, or actual engineering studies, static models, wind tunnels, with supercomputer time etc..
I'm certain there's a fair amount of padding for fed.gov cost-plus contracting in that estimate, but IMO, even the leanest and meanest private sector conversion budget for an enterprise the size of NASA would probably surprise you.