Well, it's been a few months so I suppose I should share how this test went.
First off, I removed the original lithium battery altogether. Given that the system is meant to go in my car, where I've caught temperatures near 46C in extreme cases, I've really gone cold on the idea of having more lithium batteries inside than I need.
Second, I removed the mock battery power supply I mentioned in my above post. The system actually worked fine as a power source, but it had a couple of problems. For one, since I was using the LM317 linear regulator (heatsinked), the assembly would get VERY hot, to the point that you could smell the hot FR4 material as the video recorder began to draw power out of the mock battery. This was okay, since it was really meant as a stop-gap solution to use until other parts could arrive, but I was suprised that the recorder didn't use it's 12V supply from the car more.
As a long-term solution, I created a new circuitboard using Express PCB. This board would pull in 12V from the car, and feed it into a switched voltage regulator (LM2596). I also added an Electro Static Discharge (ESD) supression diode to the 12V input as a bonus safety measure. From there, I connected the regulator output to the input of a linear regulator (I used LT1584, however another LM317 could have been used). Adding the second regulator was an intentional over-kill to make certain the video recorder wouldn't have any trouble with any switching noise from the initial regulator. The technical details on the recorder itself are limited, so I figured it was best to err for caution here. To protect against accidental short circuits, I added a series resettable fuse near the output, which was set to trigger near the max current rating of the voltage regulators. I also threw in a metal Radio Frequency (RF) sheild I had seen on Digikey. Basically, the switching regulator and all its peripheral components are under the shield. Finally, I added series diode to the final output to prevent the video recorder from attempting to charge my mock battery.
Overall, the mock battery power supply worked out extremely well; with no over-heating. I've had the whole setup running since my last post, and it's really reassuring to have my dash cameras back in working condition
. I attached a photo of the final assembly, but if there's enough interest, I can share a few more details on the build.