When one is stuck, one needs to think laterally, looking at possible siblings. For Jill, some of the detail dug up may not be relevant, but for Linda it might be. And among the chaff may be the grain of wheat for which Jill has been searching for four years!
I don't think Thomas of St Neots is Jill's (but he might be Linda's), but Thomas of Abbotsley might well be connected to Jill's William.
David