In a BGR, there is going to be 2 loops.
The Positive Feedback Loop,
The Negative Feedback Loop.
When you run the stb analysis, ensure that you are breaking the right loop. (ie. inserting the voltage source at the right loop)
Also, at the steady state operating point, your positive feedback loop should have gain <1.
Now the negative feedback loop, can be unstable as you are observing. Stabilize it by using the standard compensation methods. (Miller/Dominant pole, etc)