"An answerable question is: Would the octant that he borrowed from Manning fit into a Brandis-style sextant case?"
If the instrument was a Pioneer model 206, aka Navy Mk.1, Model 4, which were still made by Brandis & Sons after acquisition by Pioneer. If the instrument was a Pioneer model 342, aka Navy Mk. 3, Model 1, then is would look like Gary's A7. The box might still look like it would fit a sextant, or might not. I've found example photos of both style boxes fitting A7-style octants, so it's ambiguous until we know more details.