] `Lord Moira, a cousin of Warren Hastings'
] Do we believe this?
I cannot speak of other connections, but Lord Moira (later Marquess of Hastings) was patrilineally a Rawdon (or something else), and only maternally a Hastings. *If* there is a connection, it would be through the maternal line (for Lord Moira).
If Warren Hastings and his family were related to the Earls of Huntingdon (cr early 1500s) it was through a line not known to me. I had/ used to have the Clarence Roll which listed all the descendants of the 2nd Earl (who married a granddaughter of Margaret, Countess of Salisbury, dau of George Duke of Clarence). While Lord Moira and his descendants were listed, I did not spot a Warren Hastings in there. Then again, the connection - if one existed - might be even earlier - before the Hastings family became earls. For those interested, I recommend a peek at Cokayne's Complete Peerage (which is in the Library of Congress and some other major reference libraries), or in Burke's Peerage (in most major libraries in some edition or the other).
Shinjinee