What PCB fabrication methods for *prototypes* are used by professional engineering departments today?
None that I know of. 15+ years ago I also worked for a small engineering firm that did what you described above. Today, in my basement, I can layout PC boards with free or low cost software, generate a Gerber file, email those files to a circuit board house and have boards made for less than $3/sq in with better quality that I can dream of doing. Mask and silkscreen are typically included for the same price. Turnaround is between 5-15 working days depending on how much you want to pay.

It's no longer reasonable to make PC boards yourself unless you need turnaround time measured in minutes. It's so cheap that if you place a reasonable value on your time, you lose money doing it onsite.