Regarding the display, FT810, FT811, FT812 and FT813 are all the same, with FT810 and FT811 supporting only 6 bits per color.
Also the BT815 and BT816 can be used with the same code, the step from EVE2 to EVE3 is an expansion as opposed to the more severe changes from EVE1 to EVE2.
The touch engine in the FT811/FT813 works in compatibility mode after reset with single touch only.
And regarding the NHD-5.0 displays, I just opened the two datasheets.
The display parameters and electrical characteristics are identical.
And the schematics only differ in regards of the touch.
So yes, it should work to just swap the displays.