It appears we are related. I'm afraid I don't know a lot more about the Doe line prior to the William Doe (number 2 with that name) that we discussed, or the Morris line. I will email you a file that gives the outline of my relationship to the William Doe 2 who married Morris. The data for those early generations comes from a distant cousin of mine.
I can't help with your Morris Wainwright, but there might be more than one connection between our families, since the mentioned William Doe had a son (William Doe 3) who married an Elizabeth Wainwright. I guess it was common for brothers and sisters to marry between two families.
I'd be interested in any more information you might have that might shed light on the Wainwright connections, or anything else you think might be relevant.