Aaahhh , now I get your point of view. You , basically , try to preserve energy in order to extend your range. Am I right?
First let us remove fire from discussion (please , don't use words fire and house in the same sentence any more - it gave me chills). Second, bigger water tank isn't an issue here (you'll get as much AH as you find necessary for your trips - we are talking about availability of Amps ). Third, energy(in batteries) is preserved in various ways : efficiency of the system , reduced weight , regenerative braking , coasting as much as possible, pedal assist...
Let's change the analogy. If you have truck with 3.0 l engine (I don't know how much is that in cubic inches) and you want to preserve gas (energy) you can put carburetor from 2.0 l engine on it , right? It will get much better mileage , but slower acceleration (not enough power , engine over heating and lots of problems with it) and if you put some load on the bed it can even stall on some hill. Now , your solution is to put carburetor valves from 2.2 l engine on the carburetor, than from 2.5 l , etc...until you can make it over that hill with the load on the back and if those valves are smaller then it used to be, you'll be happy and if not you'll put old ones (3.0 l) back in place. That is analogy for C rating. Bigger tank on the vehicle (meaning , you can go further , not over that hill) is AH. Now , if you keep old valves (3.0 l ones) , you can still preserve petrol by driving slower , coast on downhills , not using AC (making it more efficient)...But you can make it over that hill (with a load on the back) any time , without trouble for your engine.
What I'm saying is - don't mix C ratings (power availability) with AH (power storage). If the system is underpowered (insufficient C rating) , it WILL kill the batteries prematurely and their demise will pull out more money from your pocket. We are talking theoretically , since you never measured your power consumption (it's based on assumption) , and you don't know how much is your system efficient (not very much , sure) and you try to conclude what happens with your batteries by measuring Volts and feel and eye ball.
That being said , you know that motor uses less amps with higher speeds and you drive pretty slowly. So your trouble isn't with capacity (AH) - it is in other things. With 15 AH batteries(any chemistry) you can go at least 15 mile ,with hills (and that is a fact - people do it almost every day and I know few of them) without pedaling. If you "adjust" your system (meaning more speed on the motor, with better efficiency , geared low for more torque and low driving speed and you can always limit Amp draw of the motor) assuming that everything is correctly wired(no loose ends) you can make it easily. But , even with that kind of setup , batteries must be able to deliver enough power for peak demands (which is unknown), otherwise , you'll be experiencing the same things that you did in past few weeks. I'm not saying that you should buy batts with 30 C (which people do use on e bikes - Lithium ones) just few times more than 1 C.
This concludes my posting about this subject and further experimenting with widely known issues (C rating related) is solely up to you (and your wallet). However , I would love to see you do it your way (relatively cheap and without BMS and proper chargers) and move on to other (bike related) projects and I will try to replicate your success (which would make me wrong, but who cares, if that means that I can ride for less money).
Please , don't get me wrong , I'm not criticizing, just expressing my opinion.