neeande, Welcome to CPF!
I have been seeking pretty much exactly the same thing for the last couple of months. Have not really found it, and I have researched, bought and tested quite a few lights.
The root problem here is the forward voltage of the LED is right in the discharge region of the rechargeable 3.7V Li-Ion cells. Primary Lithium cells have a slightly lower voltage (3.0V), so they need to be boosted to power the LED. Rechargeables start out above the Vf (LED Forward Voltage), Then toward the end of their charge they drop below the LED forward voltage. So they either need a more complicated, expensive and less efficient buck/boost regulator, or they go into "direct drive" where they bypass the regulation circuit and disable the low modes.
Using lower voltage rechargeables (Lithium Iron chemistry, 3.2V) helps reduce the 'overdrive', but the energy capacity is reduced even further. Runtimes are pretty short.
One warning about using unprotected Lithium Ion rechargeables - these lights are not designed to shut down at the right voltage to protect these cells, so they can be damaged by overdischarge. This can lead to venting and fires during charging. Protected cells reduce this danger but may be physically too large to fit properly in the light. Further research is recommended on this topic.
Fenix makes two "Light Engines", the boost model (converts voltage up) and the buck (converts voltage down) model. The boost engine is used on the 1xAA, 2xAA and 1xCR123 lights, and the buck engine is used on the 2xCR123 lights. Since the 2xCR123 (such as the P3D) lights have higher voltage from two cells they are already using a buck engine they don't mind extra voltage from the 3.7V Li-Ion rechargeables. In return they give MUCH longer runtimes since they have two cells. For rechargeable use the P3D may be a better choice.
There is one slight anomaly with the Fenix P3D buck regulator. For some reason the higher voltage causes the low output to be lower than normal. For some users this is an improvement, for others not. It is about 10 lumens instead of about 30 lumens (rough emitter estimates). This seems to fit with your low level requirement better than the standard Fenix low level, so for you it may be a good thing.
For emergency runtime the benefit of the two cells is substantial. If you carry the second cell you can have a similar benefit, but you might have to change cells in the dark... A second light would be a better plan, such as perhaps the L0D.
For the last month or so I have been experimenting with daily carry and use of a number of different flashlights. These include the Fenix L0Dq4, L1Dq5, P2Dq5, P3Dq5 and L2Dq5, plus the Olight T15q5 and Photon Proton PRO. Of the Fenix models I find the L1D 1xAA to be adequate in terms of light output, and it works really well on the new Low Self Discharge NiMH (Eneloop or Hybrio) that I tested with. I like all of these lights, but the L1D is quite adequate and cost effective free lumens. It is a little less light output than your stated number, but in actual use this difference is not very noticeable. NiMH cells don't present the same risks of fire, nor do most models have problems fitting in the light (some high capacity models are larger, beware). Of course, your mileage may vary..
The Fenix 4 in 1 special is nice in that you get the Q5 bin boost light engine and two bodies with tailcaps - one each for 1xAA and 1xCR123 - plus the candle diffuser, as well as the usual lanyards, O rings, tailcap covers and holster. Also included is a threaded body cap that keeps the threads clean and holds the battery in the unused tube. With this setup you can run NiMH AA for most things, and switch to CR123A when you want that extra little bit of light, or a shorter light. Or just keep the CR123A tube, tailswitch, cell, and protective cap module in your briefcase or backpack for the emergency situation after you run out of available AA's. You can also add a 2xAA body tube which will up the output to the CR123A level and increase runtime as well, for longer emergencies when AA's are readily available (and the CR123's have run out). All in all, a very flexible system.
Good luck in your quest,:candle:
-- Alan
