First, thank you for rescuing this snake!
The enclosure is looking and sounding pretty good, but your temperatures are problematic. Hopefully a fix won't be too complicated.
First - I am not sure if the basking spot temps you mention are referring to surface temps on the basking log or to overall air temperature (ambient temp). The important thing here though is that either way, those temps(105-111F) are dangerously high and you need to get those dropped. The surface temp on a specific basking area shouldn't be over about 100F. Ambient temps should never be over 90F. Ambient temps over 95F can lead to neurological damage or death, and if surface temps, present a burn risk.
But the other temps in the enclosure are so low that the snake is trying to prioritize staying warm even in unsafe temps. So you need to warm up ambient temps in the enclosure overall while also providing a temperature gradient from about 78-80 on the coolest side up to 88-90F on the warm side. The surface temp (not the air temp) of a basking spot could safely be up to 100F.
In a 40 gallon you could use a 50W PAR20 wide angle halogen flood lamp on the warm side during the day. Arcadia makes a nice one, but you can also just use generics on Amazon as long as you are sure to get a flood; you don't want a really focused beam here. You could use the DHP 24/7 to provide nighttime heat and to maintain temps on the cool side. Of course, both would need to be on a thermostat - if you aren't able/ready yet to get something like a Herpstat, most of the more budget-friendly thermostats on Amazon like Inkbird or BN-Link will be fine.
Alternatively, you could put the DHP on the warm side, and create a safe basking spot by stacking some flat slate or rock under the DHP beam. DHP are designed to allow heat to be absorbed by surfaces and then reflected back, so you can make a nice basking are that way. Then you could add a ceramic heat emitter or a second DHP on the cool side and set the temp so that it maintains an adequate cool side temp gradient.
I hope all this made sense. I am just concerned that your temps are too chilly on the cool side and dangerously warm on that basking spot. I don't think it will be hugely crazy-making to get everything adjusted, but it will require some changes and another thermostat.
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