TLDR; if you can machine 1/16", then a composite aluminum foam endplate will be just as light, but 7-30x stiffer.
Haha, it certainly does’t sound appetizing, but if we can resist eating our handiwork a brief analysis shows that a sandwich with foam is quite promising in terms of rigidity:
The bending moment of inertia of a rectangle is cubic with the thickness. Let’s define the original plate’s thickness as 8, as in 8/16ths. What happens if we replace the plate by a 1/16 Al -- 8/16 foam -- 1/16 Al sandwich?
Ignoring some scalar constants, the original inertia is 8^3 = 512. The new inertia is (8+1+1)^3 - 8^3 = 488. So pretty much the same!
But, Al is 7-30x stiffer (MOE) than MDF. So the overall stiffness leaps by an order of magnitude, and, because MDF is ~.7g/cc and Al is ~2.7g/cc for a 4x difference in density, at the same time overall weight doesn’t increase because we’ve replaced 1/2" wood by 1/16 + 1/16 = 1/8" Al.
But what if we were happy with the original stiffness but instead wanted to reduce weight? Could we try 1/32", aka 0.5/16ths?
(8+0.5+0.5)^3 - 8^3 = 217. So the inertia drops in half, but that’s okay because the enhanced Al stiffness (MOE) still makes up for it. And our weight dropped by half.
How far can we take this? Well, the math tells us that 1/128", aka 0.125/16ths, is the sweetest spot: (8+0.125+0.125)^3 - 8^3 = 50. So a 7-30x stiffness (MOE) multiplier puts us squarely back around the original stiffness. And at only 1/16th the weight. Win!
Of course, at that point we’re abusing the mathematical theory and neglecting the engineering reality, which is a) how do we intend to machine a part out of what is effectively 7 layers of heavy duty aluminum foil and b) have we utterly compromised the part’s strength and robustness?