in the belief that this is the right thing to do according to many experienced beeks.
Should have listened to the many that do!
The thawed patch on the roof is a clear indication of heat loss; a simple insulating sheet over the crownboard (as ericalfbee) is often all that is reequired. Not quite sure how many times we need to bang on about the financial pay-back - the sheet might cost far less than a bag of sugar. Your bag of sugar is now 'melting' the snow on the roof of your hive (and heat loss continues 24/7).
Your local BKA likely has mostly timber hives, not polystyrene. Really tough on the statistics when you think about it. Two hive owners are more likely to have two timber hives and their votes might well exceed the one vote from the multiple hive poly commercial beek! Listen to ITLD for instance; one vote for polystyrene, but two thousand hives (not all poly, but he does know the benefits).
Strong colonies with adequate stores will survive OK. They will simply use stores up much more quickly. Another story for weaker/smaller colonies which would definitely benefit from insulation or a smaller cavern. Of course, the risk of isolation starvation increases if the bees need to move to a new area of stores in the box, due to completely exhausting one area within a very cold period.
Inspection trays are a red herring unless in very severe weather as the bees can cluster where it is warmer - clearly better with an extra deep box over the deep ones, but that is another choice which perhaps should have been considered (wintered on a brood and a super is about the same as a single 14 X 12 brood).
Your bees would likely benefit from 'under insulation' only when the brood nest needs to extend close to the bottom of the hive?
Less than 3% does not necessarily include effective covering of crown boards, practised by lots of beeks as the norm all the year round - just as I do. Nor do I insulate my polyhives! See the problem of a simple poll?