1. Maybe time to replace the Eneloop NiMH AAs. They seem last a couple years, but even just one isn't bad.. as long as you catch it before it causes a problem with a recording. This option is assured to work and won't change anything in your regular working process, making it the least risk option, but also doesn't improve things. Does the same thing occur if you use the Powerex charger in place of the eneloop chargers except in normal charge mode rather than conditioning mode?
2. About 10 years ago I tried some EBL batteries that used a different chemistry than NiMH and promised some extra capacity. I can't recall what chemistry exactly, but the batteries used their own special charger. They weren't reliable. I don't think they were lithium. Of course my unrelated single anecdotal experience doesn't help you much other than as a reminder to thoroughly test any new battery setup, especially one that doesn't have a history of other tapers using it. The answer for me for rechargeable AAs and "9Vs" was to stick with good NiMH (such as Eneloop and Maha) and a good charger, and to get into the routine of testing after each use to catch and cycle out aging cells before they failed.
3. Have you considered replacing the 4-AA sled with a Talentcell lithium battery or some other similar "power brick"? Long and strong history of Talentcell working well for tapers. You are probably familiar with these, but if not, they are successors to the "9V DVD battery" that was a popular method of powering rigs a couple decades back after displacing SLAs. Built-in meter, simple on/off switch, and various voltage and capacity options depending on model. The ones I use feature a 12V port, 9V port, and 5V USB port. Comes with an AC wall-wart charger, but I find they can be charged from any ~12-15VDC source, and there is an inexpensive car cigarette lighter charger available. The one linked below has been very reliable for me, but if the capacity of your 4xAA sled has been sufficient, is bigger than you need with about 10X the capacity of 4xAAs. Nice to have the additional capacity if size and weight is not a problem though, so as to only run it part-way down in regular use. Last week over the course of an entire 3-day fest I used just two of those to power a Zoom F8 running 8 channels of phantom. Prior to the fest I picked up a 3rd as I was not sure I'd have the ability to recharge the two I already had, each of which I knew could comfortably run the rig for a day. The extra one insured I'd be good for all 3 days without recharging, including playback listening afterward and during the drive home, but I didn't even use it. The original one that I picked up in 2019 or so along with the F8 is still going strong, and the built-in meter makes it easy to keep a tab on state of charge. Here's the one I use:
https://www.amazon.com/TalentCell-Rechargeable-11000mAh-14500mAh-26400mAh/dp/B016BJCRUO?ref_=ast_sto_dp They offer various capacities in the same size "brick", and a few different "brick" sizes. You may be able to use one that's housed in the smaller brick size, which is about half as thick as the one linked and closer to the size of your 4xAA sled. Nice to not have to pop out and charge the individual batteries and to have the meter and a power switch on there. Note that over the course of full discharge, the voltage out of the 12V port drops to a minimum of around 9V or so.