Sorry TP, overhang can be a real problem.
Calculating if and when the overhang will support itself is w-a-y to complex to go into. Suffice to say if you dont support the overhang in time your tank may crack-split etc.
Once the tank is full it may happen straight away, or in one day, in one week, one month, one year, or it may never happen?
Perhaps it may never split?
It is definitely a high risk.
I for one would definitely support it. I am a carpenter and recommend using at least 1/4 inch thick timber, either man made or natural.
Man made timber is full of strong glue so is pretty robust.
MDF is strong.
To protect man made wood from absorbing water and weaken please varnish or paint. ( the first coat you need to thin by 25% to allow it to penetrate for maximum protection, use modern water based or acrylic based stuff, they are better)
If you shop around, or order on line you can get external or marine plywood which is soaked in glue to protect from water infiltration. But the end section of the board looks a bit rough as you can see the grain and ply etc. So to make it nice to look at you could glue or tack a thin length of real timber e.g. pine as decoration. Also marine ply normally you have to buy 8ft by 4ft sections.
Cutting man made wood can be a pain. Unless you have a circular saw you probably wont be able to cut a straight line.
I suggest place the edge which you saw ( and no doubt non straight section ) at the back of the tank to hide it from view. Put the professionally sawn edge to the front.
Be aware many DIY shops only sell 8ftX4ft boards so you may need to shop around.
Phone them before you visit saves time and energy etc.
Be aware Pine Boards made of nice looking and smooth pine, which look cool, are made up of smaller sections glued together and crack in time. Better to avoid Pine Boards.
Natural wood e.g. pine etc will not come in wider than 6 inch sections otherwise it warps and cracks.
MDF or Marine ply seems best bet to me.MDF will be easier to buy.
MDF is banned in America as the glue inside the board is highly toxic. If you cut it yourself please do outside and wrap a cloth, or mask, over your nose and mouth.