I am undecided about the movement. Both options are reasonable. Going by the case proportions it could well be a cal.T 17. But usually the mandatory dust cover has a metal tube attached to it which is not visible here. I don´t know if the American cases differ in this respect. Maybe they don´t have a dust cover which we usually find with cal. T17 in Swiss cases. Then it would be easy to pry the movement out. A cal. R 17.8 would be easy to access. However different with a cal. T 17 with dust cap: removing the case back will only reveil the case markings and not the movement. You must remove the dust cover and for this action you must loosen the setting lever screw and take out the crown/stem before.
This is not a job for somebody who is not familiar with it. If the screw is loosened too much it will become disingaged from the setting lever and you will hardly be able to re-insert the stem. You will have to take off the dial, etc. etc. Too great a challenge for a layman...
Best would be to let a watchmaker do the job if OP is not bold and skilful enough to do it himself.