I'm not too familiar with how the HOV lanes work in California (or in other states) although I have read and heard that it's much more strict and regulated ie, the police actively give tickets/citations for being the HOV lane without the stickers. In Tennessee (especially the route you are taking), the HOV lane restrictions are rarely enforced, so drivers that don't belong in the HOV lane use it as a "fast lane" (properly known as a passing lane). Maybe that will give some insight to more of the readers here that may not be accustomed to how most drivers are in TN.
With that being said, "slower traffic keep right" is typically true here, especially in high density traffic. I, personally, would feel safe enough driving 60-65mph in the far right lane driving from Murfreesboro to Nashville. In fact, when driving "at pace" with traffic in the far left 2 lanes at 75 mph+, I would feel less safe, especially because it's almost impossible to keep enough distance between the car in front of you, because some other TN driver is quick to jump in front of you no matter how small of a gap there is.
Again, what I feel safe doing is going to differ from you, but the main points made by other posters here are valid. Either slow down (remember a posted speed of 70 MPH is a MAXIMUM speed; it does not mean you have to drive at that speed) to 60-65mph and stay in the far right lanes or plan an alternate route.
By buying a LEAF(or other EV), I think we all accepted that we must change/adjust our driving habits and mentalities, even if that means shaving a little weight off of our lead feet.
Edit -- To give a visual to others,
here's a map from Murfreesboro to Nashville
A to B the posted maximum on I-24 is 70 MPH (25 miles)
B to C the posted maximum is 55 mph (9 miles)
I know you mentioned getting on 840 to get to Murfreesboro, but the range or more or less an accurate representation, correct?
At those speeds, I would probably be sweating with range anxiety too! I'm glad you made it though!