Warranty Repair, Much Slower than Advertised Turnaround

I recently purchased a Dell Insprion 7359 (NBK) 2-in-1 on Amazon. Within 5 days of getting it the touch screen no longer registered my touches, so I initiated the process of getting it repaired with my Warranty. While the individual working on my case ("Grey") has personally been very professional and helpful, I am very frustrated with the amount of time it has taken Dell to turn my laptop around and many of my messages (up to 2 days).

It was advertised I would receive my laptop back repaired within 7-10 days of me shipping it to Dell. I shipped my laptop to Dell on Thursday, November 3rd (the day after I received the return box). On November 9th (the date my laptop actually made it to Dell, 6 days later) repairs were underway until a hold was placed on my repair due to a part not being available. It has been almost a week since then and I have no indication on when I am getting my laptop as of today, November 15th (12 days after sending it  in; 18 days since opening the ticket)..

"Grey" was kind enough to let me know they still don't have the part as of yesterday, but I am still very frustrated and worried. I need this laptop for work I am now falling behind on. I am going on business trip to China in the very near future (this weekend) and need this before I leave, which means if it is much later I may need to reschedule the trip. 

I realize that parts backlogs happen in every organization, but having no idea on when I am getting this computer back other than "soon" is incredibly worrying, especially based on some of the other posts I have read saying it has taken weeks for people to get their computers back. Is there anything that can be done to ensure that the laptop makes it back to me as soon as possible or even to expedite it?