i am currently going through all this right now, so ill try to give you a little info from my experience.
i applied for my license though minnesota, they were very fast once my application and my school requirements were submitted. took about 1 month if i remember correctly. with that said, to apply, i had to be graduated from my school of nursing because they require your transcripts to apply. once my application, transcripts and fee's were received, i applied for my AAT through pearson vue... your licensing has to be received and approved before you can apply for your AAT. once you receive your AAT in the mail, you are eligible to register to for your nclex. usually you have 3 months from the approval of the AAT to take the exam or you have to re-register (and pay the fees). i actually took the nclex yesterday and found out i passed this morning on the board of minnesota website, so it was very fast (and the pearson vue trick/ "good pop-up" works!! if you've read anything about that trick...) by the way if your planning on doing any review courses for the nclex in preparation, i highly recommend the hurst review. i actually took the exam twice, once in december and then just yesterday. the first time i didnt use hurst.. it is $300 but WELL worth the price. i also used the exam cram book that has +1200 practice questions. also, assignement, management and delegation book and i think the authors last name is LaCharity or something like that... google it if your interested and im sure you will find it. anyways... when it comes to TN visa's, im not sure if it will be different for you because you have already have one but in my case, once i receive a job offer and i have all my documents in hand (your letter of job offer, visa screen, RN license (canadian and US), and any other papers), when you go to cross the border (if your driving) or go through immigration (if your flying), at that time, you present your documents and apply for the TN visa right then and there. one day i went though the border and asked the american border guard how likely it would be that i WOULDNT be approved for the TN visa and he said as long as i have my documents and because i am an RN, it shouldnt be a problem at all. so i hope that all helps... i have spent countless hours researching all this stuff lol