L2 to TN to L2/EAD

I am eligible to get either TN or L2 visa at the point of entry. The good thing about TN is that I can start working imminently, but I don't have the freedom of changing the job. On the other hand, if I get L2 I can work for any company, but I should wait 6 months+ to get EAD.

Can I:
1- Get L2 visa at the port of entry
2- Then apply for L2 EAD
3- While waiting for EAD approval, change my status to TN to be able to work imminently
4- Once EAD is approved, change my status to L2 again?