TN visa as Engineer as Contractor via LLC??

[ith123]

I'm Canadian and was wondering if it is possible to have the following set up:
-Large University wants to hire me as an engineer for a project (actually that I've been working on for some time) but can't make me an employee for a number of reasons (=bureaucracy - if I'm an employee vs contractor they have to technically double their budgeting because they need to allocate overhead vs just pay the amount they have).
-I have a personal LLC that I own all of.
-I am having an issue (again bureaucracy) where it is difficult for them to hire me as an independent contractor, SO:

--->Can Big University hire me as an engineer for 3 years (or less?) via the LLC (for liability and bureaucratic reasons) under the TN visa??
-i.e. the letter would say, "we are contracting to this individual for an engineering project through his personal LLC "X LLC" for $x and would like a TN for 3 years?

I know there are issues with being self employed but I've heard that it's not self-employment (1099 vs W2) that is the issue but rather self-sponsorship which is not allowed.

Thanks so much for the help!

[nelsona]

I would avoid saying "thru company xxx.." Just say that they will be hiring YOU, that is sufficient, and will be paying you xxx