Buried archaeology is not like artefacts, the act of renovation destroys some of it's essence, which is the potential to recover immeasurable amounts of knowledge from it and it's surroundings, and that's a lesson Archaeology has learned the hard way but very thoroughly over time and is committed to now (though detectorists aren't) – to the extent that 99% of excavation takes place only in advance of development and loss of the asset and the remaining 1% , for research, usually involves only sampling a few percent and leaving as much as possible for the future. To the extent that, other than maybe 1 or 2 stones, EH would certainly not agree to a grand project and most archaeologists wouldn't agree to take part in it.
In the light of that, TMA calls for not one but lots of unthreatened stones to be dug up look a bit out of line with modern archaeological thinking and maybe gives the archaeological establishment the chance to look down on amateurs, which is a shame.
Let's take EKLB for example, i'd open it up simply to stop further damage, but also gain a whole load of knowledge, but i'd want it done in a totally different way to current techniques, to put it simply i'd want every grain of soil put back as precisely as possible, any finds too after examination, this would take place over several years so everything is recorded in minute detail, every soil layer bagged etc, i know that's kinds trying to put back together a broken egg but given the time it could be done now in a very systematic and sympathetic way, or we wait for god only knows how long whilst the badger and trees destroy more and more by the day.