As you can probably tell from my previous set of questions, I am sort of grasping at straws to see if there is something that I can understand that will direct to what you are looking for. I am not trying to diagnose the system, just trying to tease out if there is a situation that would result in greater than expected voltage drop.
I think that your original question has been answered: you use the exact same voltage drop equations for a VFD and for any other source. Where those calculations need to be adjusted for VFD use is in the actual frequency being used; the higher the frequency the greater the inductive impedance for a given inductance, so if you are running the motor at 400 Hz you can't use a 60Hz spreadsheet.
One _assumption_ built into the spreadsheet that you posted is the actual inductance of the circuit conductors. I believe the assumption is a standard 3 phase set in a single raceway.
It is perhaps worth continuing to dig, because you might find a reason for excessive voltage drop, or you might come up with a _wrong_ approach that gives the result that the other engineer came up with, which puts you in a position of understanding the error.
Question: how are the cables arranged for the run. You said 2x4/0 per phase, but you never said how the phases were arranged; are all the conductors in a single conduit, or do you have 2 conduits with a full three phase set in each, or do you have isolated phases, etc?
Here is a fun wrong approach: do a 'back of the envelope' for the inductance of a single wire 2200 feet long. Use that inductance in a voltage drop calculation.
When I did this I got an inductance of about 1.5mH, for an inductive reactance at 60Hz of 0.55 ohms. At 190A, 0.55 ohms puts you in the ballpark of what the other engineer got. As a reactive voltage drop you still need to do vector math to get the total drop, and I'm way too tired to figure it out.
You will note that the X value that I got was about 10x the one in your spreadsheet. The reason is that when you have all three phases in close proximity the inductance is greatly reduced. But perhaps you have 'isolated phases' in the non-metallic conduit, which would increase the inductance of the run.
-Jon