Kroll,
If you go to the Electrical Tips & Tricks thread, Post# 38, I have a diagram on how to wire a 4-way switch to a reversible motor. It may help you.
I assume that to reverse your 220 volt motor, it's a matter of reversing a couple of sets of wires in the terminal cover (see your motor name plate of terminal cover).
In my motor: Fwd = blue to blue & yellow to yellow. Rev = blue to yellow & yellow to blue. With the help of an ohmmeter, you should be able to figure out how to reverse the circuit in your drum switch.
IMO: You will find that reversing your mill is a necessity rather than a luxury. Along with the above statements, if you're drilling and your drill bit gets jammed, a quick bump in reverse will get you out of the jam. I just experienced that inconvenience a couple of weeks ago. I'm planning to wire in a reverse drum switch in my 1948 Atlas drill press when I restore it.
If you can post a picture of your motor nameplate and the drum switch information, someone can probably help you along also.
Good luck.