In all honesty, I've been in both the electrical and engineering trade for over 15 years and this is something I would never do. You've got way too many dangerous variables here; not just for your snakes but for your house. Go ask an inspector if you do not believe us.
Also, the info you provided is incorrect. Flash point of paper is around 451 degrees Fahrenheit, the flash point of (MOST) wood products STARTS around 575 degrees F, and that's after all moisture in the wood has been reduced. This does not take into consideration ink on paper or cardboard or lacquer/varnish on wood products.
You are asking for massive trouble, in the event of an accident. Electricity is not always reliable, You could have internal wiring errors in your plugs and cords that you aren't even aware of, also, you can overload your heat tape.
I am not trying to be rude in any sense of the term. I am voicing this due to my knowledge and concern for you and your animals.
I do think a safety/electrical inspector funded by your county or state can adequately provide you proper feedback if you do not want to see what we have to say here.
OK!
There's a post I'll answer to, thanks for your civility, it's a breath of fresh air!
Since you mentioned qualifications, I've been an engineer for 26 years, besides other things. I have all the tools and even a lot of the materials on hand to make a rack out whatever material I choose. Even metal or masonry. I didn't choose cardboard as a last resort, I assessed my needs, my time, and my expense.
You're point is well taken on the different flash points of paper and wood. However, I'd like to remind you that there is another major component, the plastic tubs. And some use plastic as a rack material. The melting point of plastics is significantly lower than any of the above mentioned temperatures.
In the event of an overheating incident, the chain of events would be, heat source overheats, bad things start happening to snakes, plastic tubs melt, worse things happen to snakes, rack burns.
That would be the SAME order of events for paper OR wood. The marginal difference in the flash time would already be after the damage was done.
No-one has a problem with the safety of the plastic component, so why go beyond the point of that?
And thanks, our house circuits are in order, none of the problems you mentioned!