I wouldn't rule anything out! This lot is such a mystery I've no idea where they were all from!
Beds/Hunts - no marriage (--?--) Giddings/Alice
Biggleswade - no baptism William Hayes
Beds - no obvious burials of William and Alice Hayes (yet their daughter married in Biggleswade, and seems to have stayed there until she died)
Where did you find the Bedford burial - I can't see it on the NBI?