You could combine Magic Wood with a load of other high altitude options: Chironico, Brione, Gotthardpass, Sustenpass, Cresciano, Val Di Mello, Silvretta. So you could adjust your destination for conditions/the weather. None of them will be perfect conditions by June but they are high enough that climbing hard is still possible.
Chironico would be better in April than June as there's more slopers than at Magic Wood and most of it isn't quite as high altitude. Discrete van camping is available at various car parks around Chironico and there are basic facilities (clean porter loos and water taps). Food in Switzerland is very pricey though, make sure you stock up before crossing the border!
I don't know what the van situation is at the others.