Your situation is very common, especially when using a glass tanks with an all-screen top. Your issue boils down to this: likely, the cage and room humidity is low, making the heat-holding capacity of the air very poor. This means you need high temps on the heat pad to transfer through the substrate, and then the temperature dissipates quickly on the surface.
You could always just cool the kingsnake for the Winter. In the wild during this time of year, the snakes do not have access most of the time (or all of the time depending on region) to 80 deg basking places. Most of the time during Winter, the temperature of the Earth subsurface where the kings stay is probably in the 55-60 deg F range (I've measured burrow temps where I live in Cal king areas. I don't know if kings were there, but I assume that they are subject to similar temps much of the Winter time. Warm Winter days may allow for near surface basking, but burrow temps even on warm days are still very cool. They warm up considerably in Spring.)
Anyway, back to the topic. If you raise the humidity a little in the cage and insulate the walls a little, you will not see as large a temp differential between heat pad and top of substrate. So, a wood lid with one 4x6" or whatever (just not large) ventilation screen on one side will help. Then, place a large water bowl in the cage, and a heat pad under one edge of the water bowl. Adjust as needed.
In addition, place styrene foam insulation on the back outside wall of the tank and sides if you want. That helps insulate so you need less wattage to heat the tank.
My 10 gal tank lids are made of PVC. I will post pics once our camera arrives around Christmas time. I do mount a light socket on the ceiling of one end of the lid. The lid is in 2 pieces. One piece with the light socket stays fastened to the cage rim. Only the other piece is removable for access. I use a 15 watt bulb and a small heat pad- that is it. With the setup mentioned, a 15-watt bulb will heat the cage air on one side of the cage quite nicely w/o drying the air too much. Your cage is larger and so a little more wattage may be in order. Use a dimmer!
Another idea is to use a sweaterbox cage in Winter, since ventilation in those is very low. It is easier to maintain humidity and heat as a result.