If the desire is 20mph, a 500W bike can achieve this on throttle only. A 750w can reach around 25-30mph.
Is there an opposition to pedaling? With pedal assistance most bikes in your price range can easily meet your range goal, and with the assistance of the motor the bikes are actually fairly easy to pedal.
I bring this point up because there are quite a few bikes out there that meet most of your requirements. The hangup is the battery capacity. A typical 20ah 48V battery is going to run around $550-600, which tends to bump the price of the bike up just outside of your price range. There are quite a few bikes with 13-15ah batteries that are well within your price range out there.
As for alternative options. This Himiway bike comes pretty close to checking all of the boxes.
Buy Himiway Cruiser Upgraded 750W Motor Electric Bike, 48V 17.5Ah Removable Battery 26" x 4" Fat Tire Ebikes, 60Miles Range, 25MPH Electric Bicycle Shimano 7 Speed with fast shipping and top-rated customer service. Once you know, you Newegg!
www.newegg.com
This bike comes with a 20ah battery.
Buy IMREN Electric Bike,Adult Electric Bicycles 750W BAFANG Motor 48V 20Ah Removable Battery 26" 4.0 Fat Tire Ebike 28MPH Mountain Ebikes Shimano 7 Speed System with fast shipping and top-rated customer service. Once you know, you Newegg!
www.newegg.com