I agree I think that would be your best optionFrom the pictures, it looks like EX head would fit the space physically. You would, however, need to get your hands on connector pinout diagrams for both EX and LX audio units
Here is one for LX
And looking at the pictures of EX connectors, this is definitely not a direct swap.
Additionally, OEM units tend to check car VIN for security, so swapping in a unit from another car may be problematic.
You might consider aftermarket. 2016 is far more aftermarket friendly than 2009-2015 models. Crutchfield lists a lot of double-DIN heads that fit a 2016LX and carries the faceplate frame for it.
Regular double-DINs will have a 7" screen, while Honda OEM is an 8", but depending on your budget, you can go with floating-screen unit from Alpine, Sony or Pioneer.