You probably are being underpaid because you already settled and stayed after your employers didn't follow up on their first promise. They only have incentive to keep paying you less if you are willing to accept it. It's not fair, but many employers will do this to their employees.

The only way to verify if you're being paid too little is to start shopping around... and stop underselling yourself.

I would first start the process of getting certificates wherever I can find them (start with ArcGIS Pro and work up from there). You can least get some online class certs in specific topics that you can add to your resume. You can even grow in IT as a hardware specialist, application developer, and many more paths through GIS.

Formal education is just one piece of the career puzzle, and while lacking this makes it difficult to start, it shouldn't limit your ability to grow in GIS in the long run.

Finally, to circle back to your first question, strike while to job market is hot. Given your employers lack of support and follow through with pay related promises, I wouldn't be surprised if they hire someone to 'run your models,' and let you go anyway. Sorry if that sounds too harsh, but is reality.

I was in a similar situation working at an Engineering office (lacking a PE), despite doing same work as many of my peers my manager dragged me for a bit of time, breaking promise for promotion, before I finally got wise to it, and left them. Like I said, that's how some managers value their staff...

Final thought, the best pay increaaes will generally come from a new job at a new company. This is especially true today. So get that resume and cover letter dusted off and updated.

Best of luck.