I know how desperate you can become when something like this goes wrong. The tension can be very high. And how easily things escalate. So first of all I want to say; take your time.
And maybe you can take another look at this:
The spark plug hole is in the center of a dome.

Now look at the 1st drawing:
When you let water flow through the inlet, the piece of wood is brought in front of the spark plug hole.
If there is a constant flow of water, you are able to use an iron wire to manipulate the wood so that it can pass through the spark plug hole.

I would make something that allows you to attach the garden hose to the inlet, so that you don,t have to pay attention to it.
You can also use the vacuum.
You can make a bucket with 2 holes in the lid so that you can suck up water whit out getting the vacuum cleaner wet.

You can explain to some children what is going on. They really like that kind of challenge . You can then sit comfortably on a chair with a beer.

You can also turn it into a competition with a prize.
A variation on this theme could be to let water flow through the spark plug hole and push the inlet valve open as Drag bike mike brilliantly suggests.
Once the wood is out, reassemble everything and go for a long ride.