IMO, I don't see how TTC could put full duties into both at the same time... a speculative statement on my part.
Also, I would think if you notify the count, requesting a stay, you are operating in good faith with the court, in that you are 100% committed to working on a settlement during that time....another speculative, and perhaps naive assumption on my part.
(Geez, I wish we had Ron on here to clarify - another legal person want to chime in?)
All JMHO
Regards