The voltage limit by the TVS should likly be higher than just 18 V. Depending on the driver / switch this could be more like 100-200 V - just not more than the switch or coil can sustain.
If there is a diode allready inside the coil, this will limit the voltage - so the external Zener / TVS would not work.
Lowering the current is not an alternative, but a different way to speed it up - you can use both together.
My dad is going down there and he'll look for diodes and try to detect any in the coil. If there's one in the coil I'm not sure what he can do beyond limiting the current. 18V is all I had, I'm sure it'll be better than .7v on a rectifier.
Unless you are using some spectacularly massive solenoid, chances are the few milliseconds it takes to release are:
1) many times smaller than a humans reaction time
2) Swamped by other mechanical factors (such as the hydraulic response of the transmission system to which it is attached)
You'd be surprised. I've seen not-that-big coils take a long time to release (long enough to hear). Also consider that the margin between wins and loss is frequently down to 5ms or less. I've not the seen the coil in question here, but the one the transmission brake on my dad's Vega is bigger than a can of soda.
Also I don't think the transmission is hydraulic- its a Lenco, I think. But regardless the delay in the transmission, starting that process earlier will reduce the response time!
The reason why the response time of this coil is important was explained to me, and it made sense, but I don't remember, sorry. Note that this is all part of a system of events that happen during launch, so helping everything activate at the same time is a help. I *think* he detected the latency from the coil with his vehicle's data logging.
This is a very serious drag car- its a "Pro Mod." 3500+ Horsepower.