If there's one of those that has relatively less expensive inputs and is just labor-costly because it's hugely finicky, the Project might want to practice on that. And if there's none of those with expensive outputs, they could try perfecting via Prestidigitation some processes that sell for less. If his researchers maybe want to mess around with it whenever. Rather than, you know, the boiling-acid version that should only be done in groups, and with Resist Energy cast. Keltham has given them some known chemical reactions to mess with, to see if they can steer around reaction pathways, but those reactions are pretty elementary and not that finicky to start with; there'll be some different game for mastering the trickier processes.
Their current problems along the way to completing a distilled-oil-of-vitriol production step, include:
Figuring out if they need to purify oxygen for step one, where they burn sulfur to turn it into sulfur dioxide, or if regular air works; if regular air doesn't work, they'll need to liquefy air to distill it; or use a controlled-lightning process on water to make combined Element-1 and Element-8 gas.
Also, it would be helpful to know if any of the "create a bubble of breathable air" spells work in a way where they can extract purer regular air from that, which will be useful in chemical reactions.
Either figuring out some known Golarion metal is element-23; or getting something else to act as 23 for purposes of its oxide catalyzing SO2->SO3; or directly Prestigitating SO2 in a way that makes it easily combine with oxygen at high temperatures to form SO3. They also need to know if pure oxygen or at least pure air is required for this step; Keltham suspects you can't just use atmospheric air here, but he's not actually sure.
Measuring temperatures for purposes of getting the SO2->SO3 furnace to above the melting point of water by 450% of the difference between the melting and boiling point of water. Mercury thermometers don't go that high and are kind of dangerous anyways, unless they're very certain that healing or Restoration works to solve a long-lasting poisoning problem there.