You said connecting a charger to the battery was optional, however have you tried precharging the battery since taking ownership or checking its current SOC?
Have you tried charging the battery before driving the vehicle?
Hondas have something that turns the alternator off and on as needed to aid in mpg, its called an ELD. Having said that, myself and a few Insight owners have noticed a signnificant increase in mpg whe precharging the 12 volt battery before driving on short vs long trips. After 7 miles or so the charge is worn off and mpg starts todecline vs increase.
For the Insight it cuts on the charging of the 12 volt battery when the power falls before 12.5 volts and off when it hits like 14.5 volts.
If you consider this a fail, get yourself a grid tie inverter and use it to supplement your power needs in your home. I have 6 panels and 2 converters and they save me 50 bucks a month on my power bill.
Or if you like, Ill take the panel off your hands. You anywhere near 288 and Hull St?