In general with Spectre if you are concerned about accuracy, start by setting errpreset=conservative. It loads all the tolerance settings with a rather conservative set of values.

When trying to explore large-signal stability with transient, it is important to choose a stimulus that drives the circuit into all of the various nonlinear regions of behavior. For example, I once found a high gain sample and hold that went unstable only when one of the amplifiers in the circuit was driven into slew-rate limiting.

The suggestion to use pulses rather than sinusoids is also a good one. The rapid transitions contain more energy at high frequencies that generally couples better into the unstable mode of the circuit, which are usually found at the higher frequencies (remember that the instability is generally narrow band, and you must excite it with sufficient energy within its band to get it ringing).

-Ken