Very interesting experiments, great work.
A couple more ideas for experiments. Maybe you or somebody else tried these already?
1. Place the rods "in series", creating an arbitrary long stick. Say, 4x140mm=560mm.
2. Leave spaces between the rods on the sleeve. The diameter stays the same with fewer rods, or the diameter can be increased with the same number of rods.
Combining the 2 ideas, one can make a long and wide ferrite antenna with fewer rods.
73, Mike AF7KR