First thing to try is a firmware reflash in this case.
The U1000's hard reset is actually by holding down the REC button for about 5 seconds, or until you hear a beep. May not help here if the dash cam is already turning off.
The batteries come with velcro-backed adhesives - these should allow you to stick the battery onto any surface then use the other piece to stick together with the battery pack. Zip ties may help as well.
You can get a 12V power inverter that will charge from a regular home outlet, but this...
Motion should be capturing what you described. You're sure the files of the break-in isn't in the incident recording folder?
Looking at the last (in terms of timestamp) video file recorded in parking mode, what is the voltage level reading at? You can find that in the bottom left corner of the...
The PM EZ has been discontinued due to numerous compatibility issues.
The Power Plus you have is more or less better than the PMP.
Thus, an improvement would be a battery pack like the BlackVue B-124X.