My project also builds on top of the Arduino ESP8266 SDK and everything works fine. I'm struggling now between using Arduino and the RTOS SDK. Arduino has more supporting libraries, but they are stuck on the pre-3.0 SDK, so they don't take advantage of extra RAM or handle misaligned Flash reads. So my RTOS SDK version has 42K of free memory after initialization and Arduino only has 29K. And the RTOS SDK crash dump is SO much better, giving rational stack traces.
Anyway, I don't understand why I seem to be having these problems so consistently and from searching the web it seems like no one else is seeing this.
Maybe I should focus on getting Arduino to give better crash dumps and give up on the RTOS SDK