Just to clarify, "3.6V" LI-ion batteries are the same as "3.7V" Li-ion - that is the reported nominal voltage, with fully-charged capacity at 4.2V regardless. They can be from a number of chemistries, but ICR and IMR are the most common.
There are some brands of "3.0V" Li-ion cells (typically, I think most of these are either 3.4V or 3.6V fully charged), and are often LiFePO4 chemistry (although ICR is also possible).
These lower "3.0V" rechargeable cells should give output performance closer to regular primary 3V CR123A. Non-rechargeable CR123As are actually 3.0V nominal (3.2V brand new). So, typically, "3.0V" Li-ion (nominal) will be comparable or only slightly brighter than primary CR123A initially. They are a good idea if you want to maintain proper output modes of the primary CR123A cells, in cases like this where 3.6/3.7V nominal Li-ion produce higher unregulated output.
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