Would it be possible, provided that the tube were long enough, to obtain a complete inversion, in which the entire series of the males should occupy the narrow gallery at the back and the entire series of the females the roomy gallery in front?
I think not; and I will tell you why.
Long and narrow cylinders are by no means to the Osmia's taste, not because of their narrowness but because of their length.

Observe that for each load of honey brought the worker is obliged to move backwards twice.

She enters, head first, to begin by disgorging the honey-syrup from her crop.

Unable to turn in a passage which she blocks entirely, she goes out backwards, crawling rather than walking, a laborious performance on the polished surface of the glass and a performance which, with any other surface, would still be very awkward, as the wings are bound to rub against the wall with their free end and are liable to get rumpled or bent.

She goes out backwards, reaches the outside, turns round and goes in again, but this time the opposite way, so as to brush off the load of pollen from her abdomen on to the heap.
If the gallery is at all long, this crawling backwards becomes troublesome after a time; and the Osmia soon abandons a passage that is too small to allow of free movement.