One more thing. At such slow speed stepper motors can be silent. I’ve used the drv8825 (which is slightly better than an a4988 imho) at 32 microstepping (i.e. 200x32 steps per revolution) and it is quiet and costs about $2. Perhaps the current needs to be reduced? A4988 and DRV8825 have a little pot to alter the current. My drv8825 are typically paired with a nema17 which comes in a range of thicknesses.
If you want to get fancy - you could go for one of the silentstep trinamic drivers used in newer 3d printers (e.g. TMC2209) but they are more like $10 and I can’t tell you if they are easy to use.