Yes, no other heat would be required. Even now, I'd be concerned with the bulb in the tank. You are absolutely sure there is no way snake could touch it?
20long is generally accepted as about the smallest size you'd want to house a full grown snake in. Big as you can afford to go would be best. Don't need to worry too much about height, large surface area is what you are looking for.
I totally agree. Even the smallest snakes can reach the top of a viv to escape, so yours would have no problem reaching the bulb.
I put all my adults over 500g into 55 gallon tanks. 20L is the smallest that is recommended, but you also have the options of Sterlite or Rubbermaid plastic bins, the kind that you can slide under your bed can be more than large enough for an adult.
Definitely get a larger UTH, and here is a tip for its use. Take a sheet of aluminum foil at least twice the size of the pad, remove the sheet covering the sticky side and place the sticky side on the foil. Fold the top and sides over it, making a neat little packet. Now you can tape the foil-wrapped UTH under the tank with any kind of tape and when you want to remove it to put it on a different viv or are immersing the viv in water to clean it you can just cut the tape and if the foil tears it's an easy fix. This way the pad and the wires won't get damaged and you don't have to purchase another UTH. Also, the aluminum doesn't hinder the heat in any way.
Also, noting the shape of your viv, even if all of the UTH doesn't fit under one end that's okay. I have used larger UTHs under 10 gallons for babies and left 1/2 of the UTH exposed. The thermostat regulates it so regardless of the size it will still hold a nice 85° to 87° temp on the warm side, the cool side will gradiate down to around 75° and even if it is cooler, that's okay. Just have plenty of hides around the viv to let the snake choose where it is most comfortable for them.
I hope this isn't too confusing, let us know if you have any more questions, but it sounds like you are going to do great!