Hello Findem (and Martin) ......
It's a pity about Boyds. It would still be worth Martin checking though, as he seems to have a slightly different line.
Again, I hope I'm not teaching mother how to suck eggs, but ....... I did have a quick search of the National Archive Online Documents service (
http://www.nationalarchives.gov.uk/documentsonline/ ) using "Eve" for 1600 through to 1750 and found a couple of intersting looking Wills. If you haven't been there recently I recommend you have a look.
One Will struck me as particularly interesting, that being for Thomas Eve, Yeoman of Chignall St James dated 1666. I know it's 50 years earlier than the time of your 'missing' Thomas Eve, but the proximity of High Easter to C St J and the traditional use of forenames makes it of some interest I'd have thought. There were a couple of John Eve Wills too.
As most wills mention children, so you may be able to work 'back to front' to get to your ancestors.
Certainly worth a look and may be worth the £3.50 a shot to look at one or two.
Aye
MiddleEnglander