Damaged TPL7407LA Transistor Array (*Updated With Scope Testing Images*)
Unlike bipolar transistors, mosfet input stages are high impedance, which is usually an advantage but sometimes carries disadvantages as well. In noisy environments like automotive applications, there are often energetic transients coupled into lines, and the higher the impedance terminating the line, the more voltage produced by the energy of a transient.

What is needed is a means of dissipating short bursts of energy, and clamping diodes are excellent at the job. Diodes are quite robust and it's difficult to damage one in short spaces of time.

I suggest you try clamping each of your inputs with at least one diode, cathode to input and anode to ground. That will limit the negative voltage excursion to a diode drop below ground and allow the energy of any transient to dissipate in the diode.

As you found, trying to use a diode to block a transient presents it with a high impedance which cause high voltage spikes until the the transient finds a way to dissipate its energy.

If you want to be quite sure, you can also use another diode, anode to input and cathode to a positive rail to clamp the the inputs' positive excursions to one diode drop above that rail, although the TPL7407 datasheet indicates it has over-voltage protection on its inputs. In any case, you are usually better off allowing spikes to be dissipated in cheap, robust components like diodes, rather than inside an IC.

I understand that adding extra components partially defeats the point of using an IC for your low-side driver, but a few diodes in the right places can save you a lot of grief.