In order to answer your question I have to ask a few questions.
What is the diameter of the capstan? Is the capstan motor direct or belt drive? If belt drive what is the drive ratio? Does the capstan motor have feedback? Is its speed regulated?
You didn't say what this is for but I'll guess. "3.75 ips", "double speed"?? Compact cassette?
Reel to reel tapes run 30, 15, 7.5 3.75 and 1.875 ips.
8-track 3.75 ips Compact cassette 1.875 ips Mini and Micro cassette .9375 ips.
".small motor that turns at 1600/3200 rpm"? Multiple windings or different voltages? No load speed? Motor speed will vary with the load.
If the motor you have runs too fast you could try reducing the voltage with an adjustable voltage regulator or resisters to reduce the speed.