JohnInKansas,
Thanks for the reassurance about the lead.

I went out today to several stores that sell paint and asked about the safety of the paints that looked to be suitable for my purpose. I was told that, by government decree, oil based paints will soon be a thing of the past and that any oil based paint in a spray can will contain solvents which may be harmful to widdle kiddies. I bought a litre can of a gloss latex paint that the seller swore up and down has nothing harmful to children in it and will stand up to hard use and weather.

I will sand and try to paint over the old paint which is thoroughly dry now. It's cloudy, cool and was drizzling briefly a couple of hours ago, but it's supposed to be sunny and 25ºC tomorrow, (that's more than 70ºF, which is 20ºC), I'll paint it then.

The children in question will be here on Friday. I'm hoping by then the overhead ladder will be evenly covered in the guaranteed-not-to-harm children paint and will be thoroughly dry so they will be able to use it and I will be able to focus attention on how long (wide) bracing must be to to keep it from tipping over sideways when the ladder is used improperly.

Thanks, everyone who tried to help.
rags