David,
Probably best to do it outside of ArcGIS. If the TIFF format output of your scanner was Exif compliant, true for most newer scanners, you should be able to rotate the images by editing the Exif orientation & issuing rotate/flip--a lot of applets (including the scanner controls) to do this with. By nature this will be lossless--90, 180, 270 degrees.
But, if you need additional touch-up of the scanned maps while rotating--use open source GIMP or Adobe PhotoShop. Note that any rotation other than 90, 180, or 270 will "resample" the pixels. The 64-bit versions of programs will allow you to handle larger TIFF images.
You should be able to script the rotations. GIMP provides the Script-Fu macro language or GIMP-Python with an extension. PhotoShop has Actions macros or scripting with JavaScript or Python (w/the Photoshop.Application COM server)
Of course when you bring the reoriented TIFFs into ArcMAP, to do any useful work when you georeference you will be transforming and resampling anyhow. But if you work in the same projection an AFINE transform with just 3 control points will give you good registration with simplest pixel rotation and scaling.
Stuart