I'm confused, what is $160 at carparts.com?.... certianly not a new OEM dashboard, they list for around $700 to $800 if I'm not mistaken and it takes several hours to install one as the enitre dash facade has to come apart along with the center console, etc., it's not something you would want to do yourself unless you've done it before or you're very good at taking things apart and getting it back together correctly, a few people have had to go back to the dealer because a tech messed something up, broke something or left some wiring not connected, etc.while doing the R&R.
That all being asked and said, it's possible that you can get it transferred, but I have read of other people that moved while waiting and tried to get it transferred and was refused and had to re-inspect and reorder at their local dealer and get back in line, so if they won't transfer the dash order, I would suggest going to your local dealer and get the inspection and dash ordered and get in line, either way this needs to be done before the deadline.
Edit, I just went and looked up the dash "cover" at carparts.com, and you're correct to a degree, it is $160+ and yes that dash "cover" is easy to install because it's not a OEM dash board, it installs on top of your existing dash board with double sided tape or similar method, it is a far far cry from the one you would get replaced by Toyota, I would sugggest not going with that option and persuing the OEM dash replacement through Toyota, you may have to wait a while to get it replaced but your dash will look brand new and not just a coverup, also if you look at that dash "cover" you will see a cutout that over the glovebox area, that's done that way because of the airbag that is covered by the OEM dashboard and the dash "cover" will not let the airbag deploy as the OEM dash does, which is designed to allow the airbag to deploy through the dash itself, you will see the old OEM cracked dash where that cutout is!!!