For a moment there I thought this might be about me as I am having a machine picked up tomorrow and going to TX via STI. I sold the machine on 11/30 and for reference I got a call from the scheduler 2 days after the shipment was booked, and they had the following day and 3 days from then available for pickup.
There are a couple variables involved when shipping with STI. First, you have to understand that STI uses regional subcontractors and some are generally more competent than others. 10 years ago in PA I would deal with A. Santini Moving as the STI sub, out of NJ. Many of those guys would show up un-announced, lie all the time, etc. Then the sub changed to Clemmer Moving which was much better overall, although because I was considered slightly more rural they had less days available to come my way. Where I am now in FL I deal with King Logistics as the sub and they are somewhere in between...nice guys that always call ahead but sometimes hard to reach the dispatcher/scheduler or I don't hear from them for 3-4 days, so I'll often call them to schedule. Oh and I have to ask them really nice to wrap and leave the blankets on the machine rather than taking them off at the warehouse. But this is me, who knows STI well and has used them for hundreds (maybe a thousand+) shipments.
Depending on who your seller is, what their schedule/availability is like, and their local subcontractor it is hard to say what a reasonable time is or what you should do. If your seller has a day job it can be tough as most STI subs only come during the day on weekdays and in my experience they generally don't call you every day to try and reach you.
I would say that you know your limits and if the seller is not able to go out of their way to make the pickup work within your timeframe/patience limit then your only real option is to cancel the shipment and perhaps the sale. Good luck!