I think their rationale is crap; the primary reason behind their valuation is that I have no leadership experience. I would be a 'rookie' supervisor with no more value than a 4-year grad coming in off the street.
This is a fair assesment on their part until you can prove otherwise.
they don't give me credit for the 'global' projects I've led to complete success (completed on time, under budget, all goals met, blah, blah, blah).
This doesn't have anything to do with leadership, your job was to keep the project on-track and you did that nothing more. Not to say that you didn't use leadership skills to keep it on track, but this statement doesn't address that. When you look at the project from a 50,000 feet view then you aren't demonstrating your skills you are collecting statistics, and unless you have a massive number of them then you have no real data. But if instead you look inside Project X at a specific point when the project was at risk, Then demonstrate the risks and the subsequent actions you took which turned the project around and thusly earned/saved the company Y dollars. This is how you can demonstrate leadership and business value.
I know individuals in my field who wouldn't even talk to these folks for a starting wage less than 25% greater than what I'm currently making.
You are either (1) not worth what these other individuals are (2) working for less than your value. It is quite simple. Simple but irrelevant. The fact of the matter is that you are making what you are making because at some point you made a decision that either made perfect sense or not a lot of sense. The only way you change that is to present the business case and hope that you presented it well. These other individuals have different skillset different experience to draw on and different abilities.
How would I go about gathering that kind of data, from reputable sources, that would even stand a chance of these people's paradigms?
One final thought, you aren't going to win this one with salary surveys and similar data. This is not how compensation is determined. Factor 1 - Companies Budget, Factor 2 - Employee Requirements. If they have budget to pay 2.4M annually but you are willing to work for 50K, they are not going to split the difference with you, and they shouldn't, they will pay you the 50K you require and pocket the rest. Now considering you are an existing employee you need to demonstrate the value that you bring in order to be able to change your requirements. So don't worry about what others are making. Worry about the value you are bringing to the organization then once you demonstrate that then the company will be far more likely to shave off some of that and let it fall on your plate.
And for goodness sakes involve your soon-to-be new boss, he can make all of this go away if he wants to. But he won't do it without a reason.
How come everyone's going so slow if it's called rush hour?