That the btree doesn't benefit from overlapping adjacent lookup/inserts is intereting.
I suppose it is because btree access (here) involves data-dependent branches, and so with random access you'll get about L mispredicts per lookup in an L-deep tree, so adjacent lookups are separated by at least one mispredict: so adjacent lookup can overlap execution, but the overlapping is useless since everything beyond the next mispredict is useless as it is on the bad path.
That's probably at least true for the small map regime. For the larger maps, the next iteration is actually very useful, even if on a mispredicted path, because the date accesses are at the right location so it serves to bring in all the nodes for the next iteration. This matters a lot outside of L2. At 5 instructions per comparison and 32-element nodes, however, there are just so many instructions in the window for 1 lookup it's hard to make it to the next iteration.
So b-trees benefit a lot from a tight linear seach (e.g. 2 instructions per check, macro-fused to 1 op), or a branch-free linear search, or far better than those for big nodes, a vectorized branch-free search.