Hi waraich90/Mosaic,
From the perspective of applying for both EE and AINP, I would say 'go for it!'. I applied last year in May for AINP nomination and heard back from them n March that they needed copies of my previous work permits and then they extended my WP for another year. I anticipate nomination from them in the fall-possibly?
With regards to EE, I had nothing to declare in respect of 'have you received a nomination from a Province' because at the time I applied, I hadn't and to date still haven't. I'm not breaking any rules to my knowledge and I haven't seen any posts here to tell me anything different.
I may attract controversy from some who might say that I'm taking a place that somebody else could use, my reply to that is along the lines of 'I'm waiting to become a resident just like anybody else. If I'm breaking any rules then I won't be the only one getting my legs slapped'.
In short Mosaic/waraich90, use every option you have.
In regards to the gap in work, I believe that it is based on hours so if you were working 12 hour days, 21 days on and 5 off you would probably be safe. The math works out at something like 1,920 hours in a standard working year where you have 4 weeks vacation and work a 40 hour week for the rest of the year. It may well be that you are very close right now and by the time you get your AOR, you will qualify so don't lose heart in that respect.
Your LMIA would depend (I believe-moderators please step in here if I'm off the mark)on your work permit. Mine is specific to my job so I do need an LMIA but if your on an open WP, you may not need one? A contract from your employer would certainly help as you will be required to show letters of employment for both past and present employers and the current employer will need to state how long your present employment is for.
Good luck to both of you. 8)