Hi Bob - yes, that's a tough one.
Over here we call our top covers (inner covers) 'Crown Boards', and most of my Long Hive Crown Boards are in two sections - such that I can remove the back one without affecting conditions in the brood nest at the front. I then crack the front Crown Board seal to loosen it, but leave it in place.
There's normally an adjustable partition board in position, so that's removed, as well as any frames I can easily access. Then I slide the front Crown Board forwards a few inches, and pull another frame out from behind it, and so on, until the brood nest is finally exposed at it's side. I then push one or sometimes two pre-drawn brood frames up against the exposed brood frame, replace the frame which was originally next to it (which invariably has pollen and some stores in it), sliding the front Crown Board back into place as I go. I then add a couple of frames (with stores if available) and finally the Partition Board. That way, during the whole procedure the lion's share of the brood nest is never exposed.
At a much later date, on a warm sunny day around mid-March or early April, I can then fully expose the hive in order to move the whole brood nest to a more central position, and continue with brood-nest spreading - usually at the side of the brood nest, because our Spring weather can be so unpredictable. I can't remember the last time one of my hives swarmed - but it was a very long time ago. A completely different climate to your own, of course.
32 deep frames in a 4ft hive should be perfectly fine in your location - (just checking)
'best
LJ