The choke is simply a wire wound around magnetic core - usually either ferrite or iron. If it's mounted on the motor, if there's access, you could migrate it to the controller (so it's still in circuit, but mechanically separate and not subject to vibration) That's the only way I'd suggest testing live. The choke is a "good thing" - it'll help to suppress high-frequency, high energy noise coming off the commutator - wouldn't recommend running without. You can replace the choke - obviously it needs to be suitably rated, value isn't quite so critical (+100%/-25%) - if it came down to it you could wind your own - plenty of resources to explain how online.

But, the behaviour you describe - "it was not long before...." - suggests the problem isn't immediate - but after a period ("not long") of operation - my money is on a temperature-related fault in the controller. Now here's a question - does it similarly fail under no-load? (on a lathe I'd suggest removing the chuck, or the drive-belt, or whatever to remove the mechanical load on the spindle and therefore the current drawn. If it works off-load, but fails under load, that's really a strong indication of the controller failing. If it fails off-load as well, then depending upon buggerance of strip-down, I'd be inclined to get everything together on a bench, video it, and send the video to the supplier and ask them to explain.

If it helps for bench-test - I could post you a (100mm dia, 180VDC spindle motor - only 1/4Hp, unfortunately, just to bench test? (an excuse to post back your old controller at the same time!).