The only solution appears to be to replace the hardware module with a 60Y3303 or 60Y3305 Bluetooth 4.0 module. You can reinstall the drivers, but they'll be removed at the next reboot.
Update: As of spring/summer 2019, Windows 10 will remove the drivers for the BCM92070MD / 60Y3271 Bluetooth 3.0 module that shipped by default with many Thinkpad X220 laptops. Bluetooth on the Lenovo Thinkpad X220 with Windows 10 - Andrew OakleyĪ Bluetooth on the Lenovo Thinkpad X220 with Windows 10