From the 2 contracts I bought through TSS, the amount of time to close seem mostly gated by the seller's getting their papers signed and sent in. In one case it went extremely fast. The other case the sellers were getting a divorce and couldn't even get together to get things settled. I was approaching the buyer's cancellation date and was about to cancel when they finally got it together. In talking to TSS, I think my second situation was quite rare.
Hang in there and we'll all be saying "Welcome Home" to you soon!