It worked. The circuit board was thrown out so I couldn't trace the
circuit. The only hint is that the motor says "2.5 uF" but I could only
find a 12.5 uF, 200V capacitor. I let it run for an hour and it ran
cool. Hooking them up in series with a light bulb, until it began to
run slowly, helped a lot. And Sjouke Burry's guess was correct. Thanks
to all.

Here's a working ascii circuit, in case I forget.


Forward:
12.5uF
||
o------||----------o Blue - to motor
| ||
|
AC in--o------------------o Red - to motor

AC in--o------------------o White - to motor


Reverse:

12.5uF
||
o------||----------o Red - to motor
| ||
|
AC in--o------------------o Blue - to motor

AC in--o------------------o White - to motor