Your current wage is completely irrelevant. Your compensation is based on agreement between you and the company in recognition of the value you bring to the organization. If you feel they are making an undervaluation it is because you are not demonstrating the value that you bring to the organization properly. Here are some recommendations...
1) Try to get the person you will be reporting to involved. HR usually has no idea what you do or how you do it. Your direct manager will at least have an idea, if not a full understanding.
2) This can be tricky in a low-level management because your value is largely based on your ability to control/influence others. You need to draw connections between your past actions and the goals of the business.
4) Finally you don't add value to the business by being a tech who leads, so don't sell yourself that way. You add value to the business by being an interpreter, you can make your subordinates more productive by insulating them from the push and pull of the business. And you make the business more able to achieve its goals by being able to effectively communicate technical concepts to them without making their eyes glaze over. The most important thing in this capacity is the ability to mirror someone to build a report if you are unable to do that or don't know what that means then that should be item number 1 for you to learn.
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.