Another type that would be suitable - St. Pierre Dory. I like this one, from Nexus Marine
(
https://www.nexusmarine.com/st_pierre.html)
but there are many similar designs available. Maybe a bit larger than you are looking for though. This one is 27' and 2700lbs. And it might be tough to scale it down much since there isn't much room in a dory to begin with. However they are easily driven and seem well suited to the power parameters you are thinking about. Here is an electric powered St. Pierre, based on a Glen-L design:
https://messing-about.com/forums/top...ic-propulsion/
Regarding the size and displacement... my thought is that larger, heavier boat has some advantages in comfort and seaworthiness. If the power package still works there is no downsize to a somewhat larger boat, assuming that there one has room to build and store it of course.
Also another thought on solar array size and the idea of a stowable array. To some extent it's possible to compensate for a smaller solar array by using a larger battery bank. The amount of power generated by the panels is still a fundamental constraint but a larger battery allows for more flexibility in actual use. So, for example, the target configuration from the original post was:
Motor: 1-3kW (I'll assume 2kW average draw)
Battery: 3-5kWh (assume 5kWh)
Solar: 1kW
giving something like 2.5 hours of run time and ~7-10 hours to recharge, unless running at speeds constrained by available solar power.
if the configuration were something like:
Motor: 2kW (average draw)
Battery: 10kWh
Solar: 500W permanent, 500W temporary (either as a stowable hard array or as a bimini or canopy)
Then there is the option to run at 2kW while charging with the 500W permanent array underway, and then deploy the additional 500W while at anchor. The extra battery capacity doubles the run time, allowing a longer run at a net battery draw, and also makes better use of extended time at anchor by storing more energy when the full array is deployed. The temporary array option might also allow for a significantly larger array when at anchor. Maybe an inflatable raft with a 1kW folding solar array? Could even be towable...