Note that Jackery 300 does NOT have this issue. For some reason, Jackery 1500 pulls more current than the 300 when charging at full speed on Tesla's sockets.
I realize this is a total waste, since I am cycling the 300 over and over again while charging the 1500, but at least 300 is much cheaper to replace and I only need to carry 1500 while we are traveling which is few weeks per year, although once we both retire in few years, this will happen much more frequently.
If the PRO versions don't show this issue, it could be a solution, although the battery must fit in the rear footwell, as we camp/sleep/boondock while travelling.