I see, in Scripture, evidence that, at the Last Supper, Christ instructed those present to "do this in memory of me."  So, who were those present?  Christ said he wanted to celebrate with his disciples and many of his disciples were women.  He did not say he only wanted to celebrate the meal with his male disciples.  I would suggest that command was issued to all disciples and not just the 12.  
Also, "They (the baptized) went to the temple area every day while in their homes they broke bread"  Was there an ordained minister in every home?

Peter did not see the role of the 12 to be celebrants of eucharist but said, "It is not right for us to neglect the word of God to wait on tables", but to "concentrate on the word of God and prayer."
As for married men being "incapable of exercising this ministry" please remember that Peter was married and Paul asked, "Do we not have the right to marry a believing woman like the rest of the apostles and the brothers of the Lord and Cephas?"