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It took a little while to stumble across and my understanding of bit operations is limited, but this discrepancy appears to be due to the data loss suffered when converting values from 24-bit to 15-bit and back again. As described here.
The relevant part of that article describes the conversion algorithm like so (where color is an integer in the range 0 - ...
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One strategy you can use is to make your leaf nodes "chunks" of cells. For example, Minecraft uses 16x16x16 cell chunks if I recall correctly.
This gives you a coarser granularity for caching and a slightly shallower octree to manage, while keeping most of the benefits of skipping large empty areas. The chunks can also map to individual meshes/...
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To skip all those unwanted nodes, I think what you're looking for is a sparse but contiguously-allocated octree, which can be easily indexed by (x, y, z). You also seem to want sequential ordering.
For this, with a maximal tree i.e. what you call a regular tree, we use something like Morton ordering to rapidly and sequentially index into the 1D array ...
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