I've tried putting the body above the inner cover to see if they'd move the contents down,
They will not do that.
1) One way is that you let the queen lay the box full and bees eate pollen off. Then you lift the box over the excluder and bees fill frames with honey when bees emerge.
2) You freeze the frames and crush fragile combs. You get off bee bread and you may use it as pollen patty.
However I recommend 1) case. It is easy way and doen not need extra work. Pollen is too valuable to waste.
3) You cut medium size slices from deep combs and glue them to medium frames
with melted wax.
4) You cut the whole deep frame with saw and put lower wood stick and you get ready medium frames.
The rest of comb you glue as said in 3)