The plan of Harry Tudor's one time warder - the Herbert earl of Pembroke - had been to marry his only legitimate child, his daughter Elizabeth Herbert, suo jure Baroness Herbert, to Tudor. Said Elizabeth was niece of the queen - Elizabeth Wydeville. OTL she married Harry's cousin the earl of Worcester, an illegitimate scion of the already illegitimate Beauforts. EIV dangled the prospect of the restoration of the earldom of Richmond to Harry - the title had been granted to the duke of Clarence, but he'd been executed and his titles forfeit - as well as granting his consent to this marriage, if Harry would bend the knee to the Yorks. As we all know this didn't happen. Perhaps if he's further removed from the crown - as in my TL - he'd take Edward's offer more seriously?