Somewhat obscure, but I recently bought some NiZn AA batteries (out of curiosity really).
They are rechargeable like NiMH but have a nominal voltage of 1.6V, so four of them make
about 6.5V (more like 7.5V freshly charged though, but should hold above 6V pretty well across
discharge history).
Hard to find, different charger needed, so not particularly practical, but a possible solution.