AKAI IIRC made the auto reversing tape decks with rotating heads, and had 2 azimuth adjust points so you could get the same response in both directions. They also made one with a small stepper motor in the head that was used with a peak sensing circuit to automatically align the head for the specific tape inserted, so as to get the best response. Worked best for commercial duplicated tapes where the end of the tape had a cut point marked by some low frequency clicks recorded onto the master loop. used to operate the cutter on the high speed duplicator to snip the big roll of tape and then it would use the endless loop of master tape in the cartridge to start the next copy.
Those would duplicate a 1 hour tape ( 30 minutes per side) in under 3 minutes, simply by running the speed up to 11, and using video amplifiers to handle the bandwidth, using no bias signal. Then you would splice the tapes into the premade leader only cassettes and use a high speed winder to get the tape inside. Frequency response IIRC was from 50HZ ( to handle the cutter signal) to around 5MHz.