You calculated the motive power needed at the wheel, you need more electric power than that to cover losses in the drivetrain and electronics.
I don't see the number for drag coefficient in your calculation, so thats for a 1.0 coefficient. A pretty good guess but it has a big impact if its much different.
Theres a tiny bit more power for rolling resistance - mainly tires resistance to the constant deforming. Pretty small.
The battery capacity needs fudge to be a workable design for that range. You never drain the batteries 100% - so you add some excess, often you don't charge them to 100% either (the last few % are slowww) so add a bit more, they will loose some with time and charge cycles - so add more. If, for instance, you were a carmaker that needs to warranty a vehicle's range for 2 years/4000 miles you'd need to oversize the battery like that.
You are draining them at 1.1C (that will get lower once you add the fudge capacities) No problem for lithium or nickle batteries, but Lead batteries spec their AH at a 1/20C discharge - 20 hour rate. When you drain them in 1 hour you get a lot less power than their ratings. So if its lead add a big hunk of fudge - like 35%. If you look at the detailed specs there may be a chart showing the discharge at different rates and you can estimate that closer.
So a lithium battery about 50AH, 2.4KWH, $2-3K, 25-35 KG, 10-18 Liters.
a lead battery of about 70AH, 3.4KWH, $700, 110 KG, 40-50 liters.
Maybe you build it with a 1KWH Lead battery, 30KG, 14 liter, $200 battery for 10 mile range, and show the math that you can fit a 2.4KWH lithium battery, $2-3K in the same compartment for a 35 mile range?