I did the FullGenomicSequence on FTDNA and my haplogroup is H1c1.
I have a total of 126 matches at the HVR1, HVR2 and Coding Region level. Last year before the number was quite as large I did send emails to everyone who matched me at that level. Although I received responses from probably about 50% of my matches, in no case was I ever able to find a common ancestor with any of my matches at that level. Some people had been adopted and had no idea who their parents were, some were only able to trace their maternal ancestry to a grandmother, and those who did have knowledge of earlier generations only had ancestors who immigrated or lived in other parts of the country than where my own maternal ancestors were known to have lived. According to FTDNA when you match with someone at the FGS level you have a 50% chance of sharing a common maternal ancestor within the last 5 generations or about 125 years. That has not been my own experience.
Stepping down to just the HVR1+HVR2 level, I currently have 231 matches. FTDNA says that I should have a 50% chance of sharing a common maternal ancestor within the last 28 generations or 700 years with those matches. I also sent out emails to my matches at that level, although when the number wasn't as high as it is now and again received a fair number of responses. To date, I have only been able to confirm one common ancestor but am coming close to someone with whom I matched only last week.
Even though my luck in finding common ancestors has not been great, I did keep whatever information that people provided to me with regard to their own ancestral lines. Most people said that they had never been contacted previously by any of their matches and many provided me with whatever information that they had about their own maternal lines. As a result of having that information I was able to see how several of my respondents were related to other respondents and was able to point this out to them. Obviously the common ancestors that they shared with one another lived much more recently than whatever ancestor I shared with them, who must have lived in the pre-immigration days.
In your own case, you mentioned that your earliest known maternal ancestor was born in 1863 and only came to the U.S. in 1871. Your matches probably share a common maternal ancestor who lived back in Ireland or maybe even elsewhere further back in time.
In my experience most people know much more about their ancestors who lived in American than they do about those who lived in other countries so unless you are fortunate to find a match who has traced their own maternal lines back to the old country but who also happens to have your own maternal ancestor in their tree due to her being the mother or a sister of your match's known ancestor, you are probably going to be out of luck. I hope that I'm wrong and do wish you the best.