I can easily make what you are looking for in After Effects. We do these loopers a lot at the studio I work at.
Here is my demo reel: [login to view URL]
I estimate this will take me one to two hours, with three being the absolute most. That includes both having the logo move like you want to and some background animation. If you have the Illustrator file, I can even make the logo have some thickness to it as it moves in 3D space.
If you have any further details, questions, or concerns, please just send me a message.
I hope to hear from you soon!