The soil I have access to grow in is in a seasonal wet zone, and worry about the plant getting too much water, so approximately how much of the root ball has to be planted in the soil, and how much can I leave under mulch with the plants likely to survive? I'm asking for the safe rule of thumb answer, not the all plants answer.
How much root ball has to be planted in the soil? Answer, all of it. You should replant trees to the same depth they were growing before they were moved. Deeper or shallower can both cause problems.
Rather than trying to somehow balance your tree on the top of the ground (and hope the first strong wind doesn't blow it down) choose species that like being waterlogged.
In the UK, you could plant willow and alder in the bottom of a river and they would thrive. In fact you often find them growing exactly like that in the wild. The European white birch (Betula pubescens or B. alba, not the "silver birch" B. pendula) won't mind waterlogged conditions either. But if you try something that likes a hot arid climate (e.g. juniper) you will fail whatever you try.
Do some research on species that suit your climate zone - just go and look at some nearby river banks, if you don't trust advice on the internet!