On the terminal M the controller is usually mounted differently (bolted to the plate instead of slotted into the case). Make sure you can install it properly.
I also don't think the "extra key" on the terminal is mapped to anything on the "normal" m.
Your "normal" M with drainage channels sounds like a blue label lexmark and the thinner plate might be the cause of the different keyfeel. It would depend on the age/type of your terminal M though.
As Berserkfan said, you can just pull it up. Try not to touch the contacts. They are covered in plastic on both sides all the way up until the very edge, so you have a good place to grip on. Just slowly and steadily pull it up.
Another thing to consider is IBM changed membranes at least once so there's a chance it might not work at all.
I would, of course, recommend making a soarer converter with a $5 arduino (pro micro) and some jumper wire. Cheap, easy, effective, reprogrammable, USB: it's all win.