The topic of your question is not really as related to the plywood tabletop size as it is the number (and type) of things you plan to power with it. The size is not as relevant. (a quantity of 3 4x8 boards is not huge in the world of O Gauge. It's nothing to sneeze at, but quite a few of us probably read your original post as a 34 x 8 layout, which would be quite a larger beast! )
Switches are a temporary load (aside from the indicator lights, which are of course always on), and you generally wouldn't likely need to switch more than 2 simultaneously (like if you had a cross-over from one loop to another). Maybe it would work OK for just powering 2 (or a few more) switches. 18 Volts AC is probably OK, but most switches can get sufficient actuation using a lower voltage.
Accessories will be much bigger question, as some may not like being operated at 18 volts, even if you do have enough power available. Also need to know if you want the accessories to be able to operate simultaneously, or is one at a time OK? If the later, you can get by with one transformer for accessories and adjust the voltage to whatever works optimally for each one. (might want a dual output one so you can leave the one output for the switches and the other for adjusting for accessory use)
But as Stan said, the power pack you have from your HO days has a pretty low total capacity. And if that is the one, the info Stan put the box around doesn't give any information on how the power is split between the AC and DC outputs. With the (comparitively) lower demands on the AC posts for HO, there may not be much available at the AC output.
I suggest deciding what you want to power and providing that detail, it will then be easier to suggest a good candidate transformer for your needs.
Also, you have a ZW, which has 4 outputs, are you really going to use all 4 for different blocks or loops of track? I realize it's certainly possible to put 4 independent tracks on the table you have defined, so maybe you have that part properly figured already.
{edit: I swear, I really started typing my response before Stan posted his. . It seems we came up with some similar concerns/questions though.}
-Dave