My goal is to make my desk fans slow down, even below their lowest setting, for use during winter.
If you're willing to tinker with the innards of a fan, most commercial off-the-shelf (COTS) fans use a speed controller that's either capacitor-based or triac-based. (TODO — is this actually right? I need to find more sources to confirm this)
For capacitor-based speed controllers , you could adjust the capicatance values for the high/med/low settings, or install a variable capacitor to achieve "stepless" speed control.
For triac-based speed controllers  , (TODO)