My IEC expires on December 17th, and I wont have my 1 year CEC experience until November 13th, plus some extra time for the 4 un-paid days I'm taking.
My understanding is that Ill have to wait until after this time to put my name in the pool, wait to get an ITA and cant apply for a BOWP until I get an AOR.....
This is all true. If you have assessed what your CRS score is (or will be), though, you will have a better sense of how likely you are to get an ITA right away. If your score is high enough, you could prepare all your documents in advance and be ready to submit. You could then apply for the BOWP as soon as you get the AOR.
The bad news - you would have to wait until your BOWP is issued to be eligible to work. You would have implied status to stay in the country as a visitor, but not to work. This is an unfortunate aspect of the IEC permit.
There is always the LMIA-approved TWP route, if you are sufficiently valuable to your employer.
If this is not all done before December 17th, would I have to leave Canada? Is there any chance to stay and continue to work?
You could stay and work if you were able to get a new work permit.