Here's my brief story and two cents, since as recently as half a year ago I was in a similar situation. I was not considering hiring someone to help with LaTeX conversion or typesetting (so I won't be commenting on that aspect), so when I said "similar" I meant that in a sense that I had to choose between mastering LaTeX to a level good enough to produce my dissertation report of good quality format-wise and producing it in Microsoft Word, the format, which I have used for all of the previous iterations of my dissertation artifacts (multiple revisions of idea paper, proposal and dissertation report drafts). While I had essentially relatively much more time than you have now, I still decided against ultimately converting my dissertation into LaTeX format (though I have made some brief attempts, mostly using various software programs that automatically convert some formats into LaTeX with varying degree of accuracy). I submitted my final revision in the Word format, but when it was time to submit the document to my institutional e-repository and ProQuest, I have just converted it to PDF format, using Word's export functionality and the result was good enough.
I have made that decision, considering all circumstances at hand and realizing that it would be more valuable to not jeopardize my dissertation schedules, deadlines and defense, while, at the same time, spend more time on producing better software for data analysis and other tasks. Because I understood the importance of mastering LaTeX for my future career of researcher, I decided to go the gentle introduction route and started learning enough LaTeX and various packages (which involved lots of Internet surfing and some TeX.SE activity), so that I could use some of that functionality in my data analysis software reporting modules (hello, reproducible research!) as well as in my dissertation defense presentation slides (using LaTeX/Beamer).
While most previous answers make sense in various aspects, essentially they all are missing your main point and limitation:
"My time is limited. I've got a couple more weeks to go...".
From my experience, it would be rather naive to expect to master LaTeX and a set of necessary supporting packages to be able to produce a good quality dissertation/thesis completely in LaTeX (even without fully reproducible workflow; that is, if you have some kind of data analysis part). Of course, it is possible, if you have had enough past experience of typesetting documents in LaTeX.
P.S. While I said that I won't be commenting on the hiring external LaTeX expert perspective, I just wanted to warn you that, if you will decide to go this route, it is imperative that you would be absolutely confident in a person, whose help you will use, especially, considering your tight deadlines. It is quite risky, as if something will go wrong (that person will not honor time frames or will have issues with conversion or will produce document of poor quality, etc.), you can imagine what kind of problems you might get yourself into. So, unless some people that you trust would highly recommend someone and assure about their LaTeX mastery as well as easiness to work with, I would stay away from that route for good. Good luck with your thesis and its defense!