Well I am not expert on this one but people usually change their employer after 6 months of getting green card just to be in safe side. However there is no written law that will hold you to switch the employer. I have seen few of my friends who switches their employer just after getting Greencard. Technically you can change as many employer as you want.
My best and only one answer to you would be
If you really have to change the employer so that you don't have any other choices then go for it. Otherwise just hold for another 4 months as you have already got your green card 2 months back and you worked for same employer for past 6 years. If 4 months can give you peace of mind then why not?