Exigo has a very large number of meanings. Please see the relevant page of Logeion ...
https://logeion.uchicago.edu/exigo
Using the Lewis&Short tab, you will see (para. II B 1) that exigo can mean to ‘exact’, ‘demand’, ‘reclaim’, amongst other things.
Taking all the above into account, here’s another suggestion. Perhaps the transcription is in error (they sometimes are, even in Bigland!), and Domino should perhaps be Dominus (nominative)?
In that event, we would have ...
cum septem de octaginta annos Dominus exegit
‘when the Lord reclaimed seven of his eighty years’
Meaning (as you said) that he was 72 or 73 when he died and effectively handed the rest of his 80 years back to God.
Many thanks for that. Just to get it out of the way first, I'd forgotten that the numbers 18, 19, 28, 29 etc were subtractive (
undeviginti etc). This
septem de octaginta seems to follow the same pattern, so I'm inclined to put it down to being a bit pretentious.
Having looked at the Logeion site, it seems that when applied to time or a life, the usual meaning of
exigo is something on the lines of 'complete', and I couldn't see anything more likely.
I acknowledge that Bigland did make some errors, but I'm afraid I'm going to take issue with the suggested amendment of
Domino to
Dominus. As it stands, the clause has the subject
qui, so substituting
Dominus would give a second subject (impossible) or require
qui to be changed to
quem.
As it stands,
Domino could presumably be either 'for the Lord' (dative) or 'with (or in) the Lord' (ablative).
Any chance of seeing an image of the original monument, if it survives (I haven't looked)? Maybe the stone was worn when it was transcribed?
If I've understood Bigland's subheadings correctly, it was/is inside the church, on a flat stone in the north aisle. I've no idea if it's still there, or how much it might have been worn down now.
"cum septem de octaginta annos Domino exegit"
I have just a small refinement to my earlier translation of the above. Exigo, when used with time, e.g. annos, frequently has the meaning of to pass or spend. Therefore, I suggest as a translation:
"When he spent seven of his eighty years in the service of the Lord."
I'm afraid I can't agree with this - and see also my comment on subtractive numerals above. He'd been vicar of Frampton for 12 years, and a clergyman in total for nearly 50 (rather than the 40 I wrote before), so I find it hard to accept that anyone erecting a memorial would cut that down to just 7 years. Moreover, as I said before, other evidence suggests his age was much closer to 73 than to 80.
Taking everything into consideration, then, my translation would be:
'...who, when he completed 73 years in the Lord, died on Good Friday 1680'