EDIT: conformed to template
Budget Bracket - I think it could easily run $30,000+, it's essentially converting an Insight into a VW XL1
Purpose of car - General use
Proposed basis for car - 2000-2006 Honda Insight
Engine of choice - Accord Hybrid drivetrain (2L Atkinson cycle engine mated to 181HP electric motor, 212HP combined), or if I could summon it out of the air, a miniature version with 2/3 to 3/4 the displacement to reduce weight. Alternatively, maybe the hybrid TDI from the XL1 itself.
Have options for small battery or PEHV with ~20-30 miles range. Easy 100mpg highway on gasoline alone, ability to do short trips without starting the gasoline engine at all. Common battery chemistry makes replacing battery a breeze when that eventuality comes. Battery for PEHV could be 1/6 to 1/8 the Leaf's size, very inexpensive to replace.
Transmission of choice Clutched direct drive from engine, single speed
Drivetrain of choice FWD, possibility of an electric motor in single rear wheel
Modifications required to above
Make it a trike - 3 wheels, 3 seats, longer wheel base, more aggressive rear taper, longer hatch - with the rear seat folded down, so you could maybe sleep in it comfortably. Lithium batteries moved to floor, freeing up tons of room in the rear, giving it a cavernous cargo area.
With the loss of a rear wheel, a change to lithium and the removal of the transmission, the car would probably end up lighter despite being longer and having more power, maybe 1600-1800lbs, down from 1850. With ~150+ ft-lbs torque, it would be a blast to drive.
Expected mileage 150-200MPGe, 100mpg+ on the highway on gasoline
Expected cost to build - Don't even want to think about this