also you can choose to face the changeling in Of Bajor, that gives you a defeated changeling
However when you leave the holodeck and/or turn in the mission it goes away. I've had both happen. You can try to drop the mission before leaving the simulation, that works about 80% of the time but sometimes I do still lose the changeling.
Also changelings show up in colony defense fleet action and a few of the explores in zones near DS9. However it's much harder to capture those.