After a lecture or two on the ways of creativity inside a box - the easiest and most straightforward sort of creativity that there is, which is at least worth trying in a lot of cases -
The Project - not Keltham, the Project - invents the bimetallic thermometer!
By methodology of getting together a dozen kinds of substance that change in various ways with respect to a temperature, over the requisite range, and trying to combine every way they can change relative to each other to form any kind of indicator that can be read.
Sibilla, tier-2, is the one who simply welds a few strips of different metals together, applies heat, and watches them bend slightly, as the outer metal expands more than the inner metal.
Within an hour they've got a wound-up spiral coil of platinum-gold-silver. You can apply heat in the range of most chemical-reaction steps, and watch that spiral wind or unwind a little bit per turn through many turns, to rotate and move a dial on a temperature setting they're going to calibrate.
The alchemist's vampire-bat familiar is no longer a bottleneck on several key processes! This takes the Project significantly closer not just to perfecting but to scaling its cheaper-spellsilver-manufacture methods. And beyond spellsilver refining, a whole new world of precise temperature-dependent chemical processes has opened before them! Not just for the Project, but for every alchemist who doesn't have a vampire-bat familiar!
It doesn't promote Sibilla to tier-1 immediately, but it puts her on Keltham's unspoken watch list for it; and if Sibilla doesn't get that promotion outright, she'll sure get a heck of a bonus.
And not just that, bimetal thermometers are one more thing the Project can sell! For revenue! Besides sulfuric acid! And they should maybe properly look into metal refining, too, now that they have a way to measure forge temperatures -
Yes, yes, Keltham realizes that spellsilver is more profitable and the critical step on scaling intelligence headbands and they should master that part first.