Six miles depending on terrain should be pretty sweat free if you choose that way to ride. 6 miles on a ebike is not much at all its gonna go by pretty fast.
the bike packing thing and solar I'm sure you could make it work but I cant really see it unless you are like riding a short distance than charging for a day or two. Honestly unless you can plug in or carry a spare battery for bike packing I think it would be limiting. you may live somewhere that has a million places to camp or hang out so might be different for you.
Me personally for six miles I would just ride a bike and chill leave earlier. that's maybe a 30 to 45 minute ride on a bike unless you have a mountain pass or something on the way.
plus with a normal bike you can go on endless rides to bike pack and not worry about charging.
Now if you can use a ebike for the commute and say groceries, beer runs, whatever that might make me lean back to ebike. Hauling stuff around gets better with the ebike when range is not a huge issue.