It sounds like you have a half-track Otari, very nice for making your own recordings, but I can understand why you can't find much pre-recorded material for it. The "consumer standard" for pre-recorded tapes was quarter-track, where as you said, two tracks are recorded/played back in one direction, and the other two tracks in the reverse direction, or one flips the reels.
If you like the sound of 7.5 ips playback, you might try recording some of your favorite music from CD or vinyl on the machine at 7.5 ips too. The equalization curves for 7.5 ips are very euphonic, and depending on system synergy can be very easy on the ears while retaining good detail, wide bandwidth and reasonable dynamic range.
I used to use my old Revox A-700 as my primary music playback device back in the mid-70's and early 80's, because that saved wear and tear on the old LPs.
Enjoy!
... You ran them one way, then either the machine would play it back the other way on another set of playback heads or you flipped the tape over and played it back....
I believe another name for the type of player I have is 1/2 track or inline-head. It reads the entire 1/4" in one direction and splits the two channels. My understanding of the more common 4 track is that the heads are basically reading an 1/8" each pass instead of the whole 1/4". I could be wrong though. It wou ...