You start out by saying:
Metryq wrote:
I may not have fancy degrees in math

and then you start going on about how math must relate to the real world while dismissing one of the basic tools of science.
Metryq wrote:
Math is just a language, not "truth." Math must eventually relate to the real world; simply checking that the units on each side of the equation balance out is not enough.

If the units of your equation are gibberish, then you're not getting anything useful, just gibberish. It's a basic consistency check that most theoretical physicists do to work out if their theories are unphysical  if it turns out they are, then you know what you're working on is nonsense.
Metryq wrote:
Meanwhile, another group of equally degreed and working researchers says, "It doesn't make sense to us, either. We'd like to suggest an alternative model."

If someone suggests an alternative model that actually is mathematically consistent, that's good. If they suggest something that's nonsense, and then get all defensive to the point of physical violence when it's pointed out that their theory makes no sense, not so good.