The meter was swapped out 5 years ago when I got solar, I can take a photo of the front of it tomorrow, but I don't see any markings that are obvious match-ups for the model #.
The current entrance from the panel comes in about 12 or so inches above the foundation apron into the basement. Theoretically I could cut a new hole through the stone facade (AFAIK it's natural stone) glue in a conduit for entry, then run ROMEX through it and along to the destination... I recall something about it not being to code to run Romex through an exterior conduit though and I don't want to run separate conductors. Will have to re-check the code. I definitely am nervous due to my lack of visibility into the interior side entrance of drilling anything since I don't want to damage any of the existing wire.
The sub panel feeder wire is Aluminum 6/4 that has a jacket rating of 90C. From this chart it looks like it is actually good to 55 amps.
http://www.southwire.com/ProductCatalog/XTEInterfaceServlet?contentKey=prodcatsheet3
If it truly was good to 55 amps I would just swap out the breaker at the head end if that's to code with a 60 and probably collapse my sub-panel with a couple of single slot GFCI 15 amp breakers since they do seem to exist.
That would free up a slot to then run the Tesla wall connector.
Based on how much of a PITA this is turning out to be I just might have to settle for lower speed 30 amp charging.
Or hiring a professional. I can just see the $$$ for this job.
Good point on NM-B outside, it is not rated for wet conditions. URD cable might work for you as an alternative, but what is the concern with separate conductors?
Is there space to add a second circuit through the back of the panel?
The 90C rating is needed for things like lighting fixture connections where the temp is high. For landing on connections, the 60 or 70 rating is used based on the rating of the breakers/ panel.
Great resource