To make sure that a motor or set of motors and the powertrain's gear ratio between the motor and the wheels can handle going up a steep hill we have a motor power calculator available on this page: https://electricscooterparts.com/motor-power-calculator.html
Once the top speed that can be used is determined then we have a top speed and gear ratio calculator for determining sprocket sizes on this page: https://electricscooterparts.com/motorwheelgearratio.html
Gear motors that wheels attach directly to are only available for slower speeds and they are not available for the speeds that you are designing the cart for so a chain and sprockets powertrain would need to be used.
Once the required motor or motors power rating is calculated then we can make a kit out of the parts in which all of the parts will be electrically plug-and-play with each other. Making a schematic is time-consuming and not necessary if we make a kit, however, if you prefer to wire the parts together yourself from a schematic then we can create a schematic for you at a reasonable cost.
If the grade is intermittent and only for a few seconds such as a steep driveway then you could probably get away with a gear ratio for twice the 6.19 MPH 12% grade speed, however, if the grade is continuous such as going up it for 30 seconds or more then I recommend gearing for the 6.19 MPH 12% grade speed, or using a larger motor for a faster 12% grade speed.
The smallest brushless motors that we carry are 48 Volts 1600 Watts so you could probably get the top speed and hill climbing ability that you want with one of them.
If the top speed of the 1600 Watt motor is 17.46 MPH on a 12% grade and the cart will be used on a 12% grade then I would aim towards a gear ratio that provides a top speed of around 17 MPH.
We have a 9 tooth sprocket for #25 chain (SPR-2509C) that fits the 1600 Watt brushless motor and we have an 89 tooth wheel sprocket for #25 chain. With this setup, the calculator is showing a top speed of 17.38 MPH.
We do not carry remote control parts so we are not able to build remote control functions into a kit, however, we could make a dual motor kit with two controllers if you would like to add a remote control throttle with skid steering. Or we could make a single motor kit with one controller if you want the remote control to steer the front wheels. The controllers have a +1 Volt DC through +4 Volt DC throttle input signal range.
Please let us know your thoughts and we can take it from there.
My apologies for the late reply. I got a couple of weeks behind on forum replies and am just getting caught up today.
I can make a kit out of everything that we have discussed. These 1600 Watt motors run on 48 Volts so the kit will need a 48 Volt battery pack.
Calculating the right battery pack size can be difficult on mixed terrain because the terrain could be mostly hills. mostly flat, or somewhere in between. As long as the terrain is not mostly hills then a 48 Volt 22Ah battery pack should have no problem with a 1-hour runtime.
What are your thoughts on the battery pack?