It appears the Basemap Gallery widget does not support adding basemaps with different coordinate systems. This is a known limitation according to the documentation for both the Portal/Online version, as well as the Developer version of the WAB.
Has anyone else had a need for different coordinate systems within the basemap gallery and are there any workarounds for this (specifically around the Developer edition)?
Basemaps with different coordinate systems work just fine under the Portal/Online map viewer's basemaps gallery widget. Don't understand why the limitations in Web AppBuilder...