Ken, I think that the full characterization of your Y-haplotree would be a very important aspect of, and go a long way toward, establishing the Irish origin of Darby Field. I hope the following will help you in doing that.
Bill Woods's "Rule of Three" (
https://www.facebook.com/groups/ftdna.big.y/) says that three Big Y-700 testers are needed (in addition to an original tester) to characterize (name, and determine the chronological order of, the SNPs of) a portion of a male line's haplotree: a close relative, a distant relative, and an intermediate relative. "Close" means a brother, father/son, uncle/nephew, or 1st cousin of the initial tester. How far away the "distant" relative is will determine the "resolution" of the haplotree, that is, what portion of the chronological series of SNPs in the tree will remain uncharacterized: if 7 generations or less, the chance of "full" characterization is good, but if 8 or more, it becomes increasingly less likely, using just the 3 additional testers. The "intermediate" tester will be somewhere between the close and distant, but usually, because of the average frequency of Y-DNA mutations (roughly every 80 years on average), no closer to either than 3 generations.
Currently, you have your "distant" relative, Mr. Connor, whose relation to you appears to be at least 10 generations back, and your shared (distant) haplogroup has been identified. You also have a semi-close relative, your 3rd cousin - though he has only taken the Y-67 test. In order to identify your more recent haplogroups, (though probably not the most recent, as he's not quite close enough) he will need to upgrade his test to the Big Y level. This is critically important.
Finding an additional (intermediate) cousin, somewhere in the 5th - 7th range if possible, and having him tested, will complete your "Rule of Three."
Your other two "related haplogroup" testers are probably part of your more distant family (with different surnames, probably quite a ways back). Contacting these testers to find out if their haplotrees have been at least partially characterized, could also help in your quest to establish/confirm Darby Field's origins.