Hi. Just happened to be online tonight, and thought I'd post a quick response.
Several years ago a wonderful lady from West Memphis, Arkansas (who turned out to be a "half third cousin, once removed" through my Bowen family) referred me to a great site put together by Martha Hills and Frances "Cookie" Harper: http://www.geocities.com/fcullom/
If you have not already visited that site, I highly recommend it - and there are various references and cross connections that you can get to through there. They did an amazing job with their research. That put me on the trail of Amey Andrews and some of the others from that era.
I have been away from this for a while, but try and gather information from as many sources as possible as often as I can. The hard part, of course, is verifying the information you find!
I've never come across anyone who descends from this Kirk(s) line, so I'm happy to make your acquaintance. Sounds like there's a connection to my Edith (Edy) Bowen (I descend from her brother, David). I have that Samuel and Edith's son was William Kirk(s) [named after Edith's father, perhaps], and that he married Jane Arnold. I can tentatively take Jane Arnold back a few generations to Christopher Atkinson and Elizabeth Radwell of Isle of Wight Co, Virginia - but have no information on William and Jane's descendants, or any other children of Samuel and Edith.
I'm on a work detail, away from my physical genealogy files and notes, but I do have my electronic family tree on my laptop and am happy to share whatever information I have - with the understanding that I cannot claim to have verified it all. I like to think of it as a good starting place in working a great big jigsaw puzzle. As I gather more and more of the pieces, I find that some of the earlier pieces I put together fit, and some don't - so I have to set those aside and start over here and there. It may not be the most scientific approach, and it may frustrate some people who are more experienced at this than I am. But it works for me. I basically gather as much information as possible, and try to make connections in as many lines as possible. I've made some fun discoveries with this method.
If you want to communicate directly, I can be reached at firstname.lastname@example.org
Good luck with your research!