Oh, well, if the TLE-300M says it can take up to 24V, then sure, use the series adapters. Parallel adapters have occasionally been available, possibly from online dealers or CPFM, but I didn't find them with a quick perusal. Fortunately, they're easy enough to make, as they're much simpler than series adapters. All you really need is a top and bottom plate. A nice insulative holder is icing on the cake.
In terms of shelf life, lithiums will work better than the Eneloops, although the latter do have a decent shelf life (especially compared to ordinary NiMHs). If you use lithiums, you could probably forget about it for 3-5 years at a time, while with Eneloops, I'd recommend topping them up every year or two. The benefit to the Eneloops is that if you have some sort of fancy charger or analyzer, you can test the cells to make sure they're still strong, then recharge them and replace them in the light. With primaries, you can't do that, for obvious reasons. The funny part is that Eneloops and L91s are about the same price.
For runtime of 4D alks vs. 12AA Eneloop or L91, you'd have to know the efficiency of the TLE-300M's converter, as converter efficiency can vary with input voltage. If we assumed that 1) the chemistries are the same (I know they're not; bear with me), and 2) the difference between low and high input voltages is negligible, then 4D will give greater runtime than 12AA, simply because of the fact that 4D occupies more volume (less space wasted by air), not to mention cell construction (some components inside cells have a pretty much fixed size - this usually makes it more volume-efficient to use a single cell of capacity 2x rather than two cells, each having capacity x). Now, since the 4D is alk, that means they'll have reduced capacities at high loads. The TLE-300M should (if it's a decent buck or boost-buck) draw significantly less current from an 18V (or so) batt than from a 6V batt. The question is whether the load from a 6V batt is high enough for D alks to take a significant hit, especially as the cells are depleted and their voltage drops, making the TLE-300M draw more current.
Bottom line: you should be fine getting the 3AA>1D series adapters and 12 Eneloops. Just remember to inspect and charge them every year or two.