I'm not Rob, but my vote is to thank her for the offer, tell her you'd like to go, but would like to take a rain check, as you're swamped right now. (This will buy you some time to be more awesomely awesome, but yet not reject her.)
Rob....? Oh, Rooooobbbbb?
(Ferg - I've told ya. I'm not great at advice, so wait for others!)
Actually this is an interesting conundrum isn't it? We like NO CONTACT but... she contacted you, you can contact her back. She wants to take you out to dinner, that's actually a good thing, especially if she's paying. You see we associate value to things we invest in, if you invest time, energy, resources, etc. into things, we associate value to those things and we are attracted to things that have value. So the dinner thing might actually be a good idea for this reason plus it also gives you the opportunity to style a bit. If she wants to take you out to dinner and treat, let her - it's probably been a while since she's offered to do this, I say go for it.... but there are some rules ;-)
Don't get all melty man and wussy, it's just dinner. Treat it as a casual interaction, look good, smell good, change up the style.
She associates a specific mindset & image with you. If you go to dinner looking a lot different than you normally look, this will throw her off a bit.
You see you've done a good job of this already. No contact. Packing her things and getting them ready for her to move out.
She wasn't expecting any of this.
Go out and then after that, no contact again. Remember it's ok if she initiates contact, we just don't want you to initiate contact.