I'm in same situation. I got GC through consutlancy as well. I got my GC last August 2016 but my project was ended on Dec 2016. Currently, I'm looking for a project but I'm still in big dilemaa should I market myself or go through my consultancy. I asked few people, they said soon I got GC I'm a free bird but I still have my doubt. I know it;s been almost 8 months since I got my GC but technically I only worked 4 months (August to Dec) with my consultancy. Is it ok for me to switch the employer? I still doing marketing with my old company but I always come up with different reasons when they send my dob requirement cuz I don't want to move again and again. I 'm looking for FT position applying through company sites only. I haven't put my resume on any Job portal sites.
I did research about it switching employer but I didn't find any concrete answer.