I was on the road this morning for a couple of hours, during which time I found myself mulling over your idea of a Long Hive using mediums ...
I'm mindful that there is a precedent for using shallow boxes in the beehives of Anton Janscha, way back in the 18th Century. He modified the krainer-bauernstock-offen, or 'Farmer's Hive' which was very popular in his day. Although there was some variation in size, these were typically 30"x 12"x 6".
This shows the opened hive (upside-down, which is how it would have been inspected) showing the lengthwise combs which are more representative of how bees draw their combs if given free licence to do so. As beekeepers we hang frames across the shorter dimension of a Long Hive for our convenience, whereas bees would much rather have the longest combs possible - even if this means drawing them diagonally !
This second graphic shows the modification that Janscha made : a second story to the basic box, which allowed honey storage and provided a facility for making 'splits'.
I've often thought about butting two sets of brood frames end-to-end to achieve this longitudinal format myself - the only reason I haven't is because of the exceptionally long lugs our frames have. But Langstroths don't.
So - imagine if you will a Long Hive of 'double-frame' length, with the same width as your standard boxes are long. Between the two sets of frames would be a fixed fenestrated partition supporting the frame lugs where they meet. I haven't done the sums, but at a guess I'd say that would provide a cavity for 26 or so medium frames - would that be enough ? If not you could always make a box 'three-frames' long, with two partitions.
OK - now here comes the neat bit. Because you've made the width of the lower box equal to the length of your standard boxes, you can now place those standard boxes over the lower story - crosswise - as supers. If all are not needed, then a sheet of plastic or thin plywood could be inserted between layers to blank-off unused boxes. Alternatively, they could be filled with insulation and/or used as feeder shells.
The advantage in having a full length set of supers, is that the same roof may then be used, as would be fitted to the lower box alone. This is the principle behind the Dartington Hive which has 3 nuc-width supers over it's extra-deep frames, whereas here we'd be looking at 3 or more full-width supers.
Hopefully there's the kernel of an idea somewhere amongst that lot to get you started on this interesting project.