Nothing stops you from being an archeologist, as a matter of fact, you may already be one. Most work of Archeology is done through research. It sounds like you are well read. Continue to read and think, at some point a question will come to your mind that you can not answer from research and you will be forced to work in the field. There are plenty of amateur archeologist out there, just become one. You don’t need a whip and a fedora to start. You have started, now get to it.
“There are plenty of amateur archeologist out there”
Heck, one of the most famous archeologist of all time, Heinrich Schliemann—who may or may not have discovered Troy, was an amateur. So were the kids (and their dog) who found the Lascaux caves.