The "Dual column rising gantry with moving table" design might work for you. This would allow you to mechanically counterbalance your entire gantry.
The disadvantage to this design is that you mentioned 4'x8', so unless you wanted your table axis to be 16' long in total, you'd have to make the gantry the long axis which would make it heavier, not just for the extra length, but also for the extra stiffness it would require being longer.
36" of travel makes pneumatic counterbalancing problematic. Things like rodless cylinders are not designed to take substantial amounts of weight in the Z direction.
It's not an easy design problem to come up with the ideal solution. If it were me it would probably take several hundred hours of different design iterations and 3 or 4 initial concepts whittled down to one to come up with something I considered to be a good plan. And the end result would look nothing like the initial ideas.
It sounds like you are planning to carve things with a rotary axis but for now want to carve all 4 sides individually....why bother?!? Just design a machine around a rotary axis to start with and forget about the table entirely?
For better comments you need to do up some designs in CAD and start a design thread. Ordering parts and such at this point, I think would be a mistake. Once you've got it all drawn out you are in a better position to build.
What do you think of the design
concept in this video?
https://www.youtube.com/watch?v=iRe-tn6lmEk
That's got a dual column rising gantry, which could be mechanically counterbalanced. And designed with a short gantry.