I'd imagine that your frog his so bloated because of how long he has been in the water, we will soak up the water when he is in there. The bloating or minimal eating should not be a worry to you.
However, the water level will be a worry as the little fella is clinging on for dear life as it seems. I think there is a little confusion, a whites tree frog as it is commonly named, Litoria caerula, is colloquially known in Australia as an 'Australian green tree frog'.
Your water level should not be taller than your frogs head.
I know you mentioned that he slides back into the water, but I'd imagine he is a very stressed frog right now and isn't used to all the water!
Your frog is definately a Whites tree frog, this is the care sheet which should be followed, I tjink there is just a cross of wires over colloquial species names.
Good luck
Amy