I got an Epson ff-680w but can't find any way to color correct the scans using a calibrated profile. My understanding is that this is the main thing to look out for when trying to scan in archive quality. How would I build a color calibration profile and apply that to the scanned images?
This describes a program I wrote that produces highly accurate scanner profiles. At least for CYMK printed material. Less so for scanning photos from chemical processes due to significant metameric errors intrinsic to most scanners. It corrects for a major source of scanner errors (large area crosstalk) and it also provides tools for using i1Profiler and printed targets to create scanner profiles.
You need a target for the type of calibration you want to do, either transmissive or reflective. You can find a list on X-Rite's website, or select the one you have in i1Profiler under "Scanner Profiling" in the Workflow Selector; the list is in the dropdown is labeled "Target Type". If you got a target with an X-Rite bundle that included i1Profiler, it's likely a ColorChecker 24 or 5G.
You can select the right one, and the software will walk you through creating a profile for the scanner and type of scan.
To apply the profile depends on the software you use to scan, but most software has the ability to apply a profile to the process. If you have images that were scanned earlier, you can use "Apply Profile" in Photoshop to adjust them.