There is no reason to fret over picking up 1200lb with your 4060 & FEL. The cg of your 4ft plywood is 2ft out from the back edge of the fork frame. The 32" materoial cg would be 16" out from the back of the fork frame. So 24/16 = 1.5x the forward rotational torque relative to the back of the fork frame. We don't know how far from the back of the fork frame the center of the front axle is but we do know going to the 4ft material makes a lot less than 1.5 X the rotational torque around the front axle compared to the 32" stack of material. As the other guy said, it is linear, not exponential.
No reason to see this circumstance in catastorphic terms or being all that dangerous. You are not , so far as we know, moving this stuff around on hillsides or slopes. The rear tires becoming light and lacking traction is a great hint for situational awareness. So as everyone says, put something in back for ballast -- not because of any great danger but because it improves the overall comfiort and good sense of operation. I use a 1460lb 7ft Bush Hog on the back of my MF2660 almost all the time when I am lifting stuff with the FEL, have rear tires loaded, and never have to even think about the balancing issue. If it fits your typical operation, hang a bush hog back there.
Unlike what one of the above posts said, the more ballast you have the less weight there is on your front axle (though the reduction is small.) Your loader is spec'd to handle loads several hundred lbs greater than the 1200lbs so an occassional 1200lb FEL load is not likely to hurt your front axle or bearings.