We need big propellers at slow speeds
At slow speeds we will need big propellers to make efficient use of the power we have available. Below we have a couple ways to think about why this is so, and some empirical results.
Energy put into moving water
From Newton's laws we know that for every action there is an equal and opposite reaction. The push you get from a propeller is proportional to the momentum the propeller gives some water. We can think about this in the frame of reference of the original stationary water, and ignore the frame of reference of the boat.
The momentum is: mass * velocity
The energy put into this mass of water by the propeller is: 1/2 mass * velocity^2
Because the energy goes up with the square of the velocity and the momentum only with the velocity, the most efficient approach is to push lots of water with a small velocity.
If a boat is going fast a propeller passes through lots of water and so can push a little bit on many different cubic feet of water and so only give any bit of water a small velocity.
A propeller that makes efficient use of 50 Hp at 15 MPH makes very inefficient use of the same power at 2 MPH. At slow speeds it goes through less water and gives it a much higher velocity.
An efficient propeller for a slow seastead will be large so that it can give a small velocity to a lot of water. Using a small fast propeller on a big slow seastead would take far more energy for the same push.
Power is energy/time. So the Hp or watts that we need will be higher if we do not design for an efficient use of the energy with a reasonable propeller. It would be easy for a bad design to use 10+ times more power than an optimal design.
Work done on moving boat
You can think about it in terms of work done on the boat. Work is force times distance. Power is work/time. If we have a 50 Hp motor giving us a force of X lbs at 10 Mph then to get the same total work done on the boat when at 1 Mph we need a force of 10 X lbs. If we do less than this we are not making good use of the 50 Hp.
A normal boat propeller is optimized for when it is moving fast as that is the hard/important/normal case. When you are moving fast the prop needs to turn at higher speed. Because of the friction of rotating a large prop fast through the water you are better off with a relatively small prop when you are moving fast and have lots of water to push against.
To optimize for a large force at 1 MPH you want a larger slower turning propeller.