Thomas and Job are the only two SAYRE brothers that I am aware of that are considered emigrants. Their brother William is not indicated in Banta (1901) as having lived in Lynn, MA, or Southampton, Long Island, NY. In fact, I'm not sure William ever left England.
The William SAYRE that is commonly recorded as having lived near Bedfordshire, England during the same period as Thomas and his family, was not related to Thomas SAYRE according to researchers (see Suzanne Sears thread), and several descendants having completed Y-DNA testing. William appears to be J2 haplogroup while Thomas and Job are R1b for sure, and in my research likely R1b1a2a1a1b4, same as me.
You are attempting to answer the same question that I am tackling, chiefly, descendants claiming lineage to a common paternal male can not belong to two different haplogroups within the period of the haplogroup's existence.
Thomas and Job, assuming they were indeed brothers and sons of Francis, would have had exact Y-DNA (with very remote exceptions) that transcended every generation to the present with minor mutations along the way. In fact, I am attempting to "model" Thomas' Y-DNA based on several descendants including myself, an interesting concept suggested to me recently.
To answer your question directly, one could be directly related to Francis and not directly related to Thomas. For example, Francis' brother or uncle, etc., has male children who are first or second cousins to Thomas and Job, but all will have or most likely have the exact same Y-DNA. So your efforts in accuracy are important and admirable.
When I compare Banta (1901) and Sayre (2003) to your information regarding your lineage, I tend to think there is some cross-breeding of Hirams, meaning one line has a member of the other line. But I need to do due diligence before we can generalize anything here.
BTW, if you have read Ralph Sayre's thread re: Y-DNA testing (and he and I have collaborated on this), his results place him in J2 haplogroup. Yes, the same Ralph Sayre who spent years researching his ancestry and published five volumes of work extending on Banta (1901), may not be related to Thomas SAYRE. The alternative is that I am not related to Thomas SAYRE. My point is that Ralph's research, which I have studied, is critical to thousands of SAYRE researchers and will help us locate our ancestors.
Is there any additional information you can share with me regarding your line?