So after spending a few hours on this, here's the solution if you want to disable Edge Swipe while still retaining two finger tap right click while using the Lenovo provided drivers to maintain the unique yoga features:
1. Disable Edge Swipe via the normal Synaptics settings: Control Panel -> Mouse -> Device Settings -> Settings -> Edge Swipe -> Uncheck.
2. To manually re-enable two finger tap, hit windows key + x, select "run", enter "regedit" then hit enter, and on the left pane browse to the following location:
HKEY_USERS\<SID name for your current user>\Software\Synaptics\SynTP\TouchPadPS2
3. In the right pane double click on 2FingerTapAction and change the value to a "2" for right click, or a "4" for middle click (I use 2). Also double click on 2FingerTapPluginID and clear any value it may have.
4. Next in the right pane, and this is what disabling Edge Swipe actually changes which breaks everything, find the MultiFingerTapFlags key and change it from a 2 to a 3 (it's originally a 3 before you disable Edge Swipe).
5. As a bonus, if you want to enable three finger tap for middle click, double click on 3FingerTapAction and change the value to a "4", also clear any value for 3FingerTapPluginID and set 3FingerTapPluginActionID to "0".
Unless you have multiple users, your SID is most likely the longest string, for instance mine is "HKEY_USERS\S-1-5-21-1669614795-426116693-2193257368-1003." Enjoy.
