Odd crash symptom related to battery

I have a well-cared for MBP Late 2013, 15” retina, which I use very heavily as my main machine for code development and testing. Since original purchase I’ve had the battery replaced twice by Apple, with no issues. Recently I’ve needed another replacement, but Apple no longer services this MBP model. As far as I can tell new OEM batteries no longer exist anywhere on the planet- only “fake” replacements. I’ve tried three different replacement batteries over the past three weeks- two generics bought off eBay, and most recently the iFixit replacement battery kit. In each case I’ve then exactly followed the vendor instructions for “calibrating” the battery (which were somewhat different..). I’ve also reset the SMC and PRAM multiple times.

All three replacement batteries behave identically. If the machine is under a steady, fairly heavy, load (running a pretty intense numerical simulation), then the battery drains smoothly from 100% to completely drained shutoff. As long as the heavy job is running I can use the MBP for other things and it behaves just as you would hope and expect. However, if I’m only using the computer for simple, non-intensive things such as editing text files, general web surfing, etc., then the computer will randomly hang or crash, usually within 5-10 minutes of use and regardless of battery charge remaining. When the machine is on A/C power, it does not crash- at least it doesn’t crash once the replacement battery has been through a couple of charge cycles.

This seems really strange, at best.. Any ideas? It is certainly a waste of electricity to have to keep a number crunching job running in the background in order to avoid crashes! Not to mention the battery life is pretty short while running the intensive simulation :)

I’ve attached the System Report battery info and coconutBattery output above. Note these snapshots were taken after draining the iFixit battery and just starting recharge. But, at least so far, the battery does charge to the 9248 mAh shown in the screenshots.

I’m certainly not hung up on “OEM”. I just want my computer to work correctly. And I’m not trying to go cheap, save money, get by with eBay, etc. But Apple no longer services this computer, and I’ve seen online that Apple no longer has any batteries for this model. So what to do? I don’t know where to get a “good” battery- “OEM” or otherwise. The two I bought on eBay and the one from iFixit appear to have essentially identical issues, and are almost unusable. I don’t think anything else is wrong with my computer, as I’ve never had this somewhat weird issue before trying to replace the battery. Unfortunately, I threw away the old, mostly degraded Apple battery. I now wish I’d kept it, as at least it ran the computer for 45 minutes to an hour of light use, and didn’t crash.

Again, the really, really odd thing is that if I have a solid background job running that pegs one of the cores on the quad-core i7 CPU, then the machine is perfectly stable running on battery power. That’s got to be a big clue?

Here is the output from TG Pro. There are more temperature sensors if you scroll down below the ones shown in the snapshot. But all of them are “green”, and below their respective max temperatures. I’m not sure what the “Last Shutdown/Sleep: PSU Warm Reset” means. Presumably PSU is the power supply. Is the fact that Diagnostic is “yellow” an indication of a problem? This output was generated while the computer was on A/C power and running the background number crunching job I described earlier.

Thanks for your suggestions and help.