Thanks, Stephen.
I thought exactly the same, but a friend of mine brought this statement from the judge list to me:
When the Flip Effect of YOUR "Invader of the Throne" activates, YOUR
"Invader of the Throne" is given to the opponent, and your opponent gives
you the monster you selected to gain control of.
The 'and' here was interpreted as a 'then'. Well, that could be corrected. My friend said that, even if the control switch of monster were to be done at the same time, it should be a requisite to have at least 1 free space in the monster zone. It was a valid point, since control switches like Change of Heart obviously require at least 1 free space, but I don't know.
In the case that both monster spaces were full, the idea of using Change of Heart is invalid. My friend said that the same should happen with Creature Swap.
I would like to hear some opinions about this. Need some arguments.