I started my work day by taking apart the Otari with the hex screwdriver, and then, for over an hour, tried to find the internal switch to go from 15ips to 7.5ips. After I decrypted the manual (on page 5-5, "big P.C.B. Ass'y"="big printed circuit board assembly"), and found the corresponding location referred to in the most basic diagram the manual refers to, I was able to start to digitize the reels. However, unlike most small reel players, you do not depress the external button, you just flip the internal switch. That gave me a pretty interesting recording before I realized it was playing at 1/4 speed. I'm creating internal documentation for anyone else that might have to digitize anything if I'm out for some reason because I don't want to give anyone the headache I've had the last two days!
Screenshot of the diagram and photos of the internal switch: