I'm sorry this happened to you. For such a simple item, racks can be challenging to get dialed in.
If the tape is running more than 20 degrees above the thermostat setting, I would suspect that the thermostat probe is either not properly placed, or is damaged or defective in some way. Judging by the fact that the pic in post #4 shows the probe reading more than 2 degrees lower than the setpoint temperature, this is likely what is happening. If the probe is not (properly) contacting the heat tape, the tape itself will get much hotter than the thermostat thinks it is, causing melted and burned heat tape.
Also, I've found that in order to (re)apply aluminum tape to heat tape, I absolutely have to remove the back of the rack in spite of having very long arms. The quality of the taping job (very smooth, no ridges) is very important to safety and tub movement, and I can't do that from the front of the rack.
If it were my rack, I'd get all new tape (since it seems the tape has been running at full power for some time), disassemble the rack to install the tape properly, and find a level solid place to put the rack.