No way would I trust that meter for anything near 1000v. Even if the meter itself is ok, your putting your life in the hands of those HongKong test leads.
I second that...
But would personally risk it with a piezo element used in a starter...
In any case. Take a look here :
https://en.wikipedia.org/wiki/Dielectric_strength
For an electric starter to work, it needs a spark. The spark needs to travel through air... so, if you know the distance, you can figure out the minimum voltage that may be required for the spark.
We can also work backwards if we know the voltage, we can determine how far a spark can jump.
The page I linked shows Air at 3Mv/Meter ... That's 3 Million Volts per meter, or 3000V per mm.
If your meter is rated at 1000V, then anything that can make a spark over 1/3rd of a millimeter will damage it.
My digital multimeter is rated to 1000V DC, but we all know that when we exceed the amperage a Fuse blow up and you just have to change it , However in the Voltage testing we don't know what is the first component that will fail if Voltage Exceed the limit, so if someone know, please tell me ....
Remember that a spark jumps through air... there is nothing stopping it from jumping across parts or traces within a device... This is why static discharge can be so nasty. Your voltage spike from the starter could have directly damaged a component in it's path... or jumped to another component and damage that.
I'm willing to bet your meter is toast.
Expensive lesson learned.