I want to make a lightweight lid of aluminum flashing (.010 thickness) for an aluminum mug (an Imusa mug which is 3.9" ID). I'd like to take the mug and lid backpacking, and be able to boil a bit of water in the mug for rehydrating meals. The lid is the sort that sits down into the mug about a quarter inch, then toward the edge bends vertically up, and then bends back to horizontal at the edge, to sit on the rim of the mug. Here's a photo of someone else's lid--perfect, exactly what I want to make. (If I can't make one myself I may have to buy one from this guy, who apparently possesses an IQ about quadruple of mine.)

I thought about how I might bend the desired ledge into a circle of aluminum flashing, with the tools I have, and came up with the idea of (left to right in photo) a "fulcrum" with pivot screw for holding the lid at its center, allowing it to rotate; and an "anvil" and "presser foot" which would bend the edge into shape. The orientation of the lid is upside down during fabrication, and the mill is turned off--nothing is spinning here(!), except for the lid blank, which I turn by hand on the pivot screw as I work around the edge.

The anvil is radiused (along the Y axis, you can see it) a little under the dimension I need, at 1.75 in. The presser foot does not have a similar radius (a problem?), I left it square, as you can see. I use the quill of my mill to move the presser foot up and down (Z axis), gently, while slowly rotating the blank. There is a horizontal (X axis) space between the hammer and anvil of about .1 inch, which I've been keeping wide, in hopes it will allow gentler bending.
Regarding the sharpness of the working edges themselves (both anvil and presser foot) they are only slightly filed.
Feeding the blank around in a circle, I'd take maybe 20 very small presses (the slightest bend appears), then on the next rotation, 20 more light presses (a little more bend), each time pressing only the amount that the metal seemed willing to give. I worked at an agonizingly slow pace.
Result after maybe 15 rotations: Miserable failure!

Even when I try to gently massage the desired rim onto the blank, I get all kinds of problems. First thing is that the blank starts to warp or bow, popping into different non-flat curves as I go around. If I keep up the work, I start to get wrinkles at the lip. And if I forge onward, I eventually open up a circular rip in the lid, like a can opener would do.
Clearly I'm doing at least one, and possibly, several things wrong. I think I am stretching the metal so there is "more of it" around the rim, which must be causing the warping and bowing. I'm considering radiusing the presser foot to see if that might help. I think there'd be less metal stretching, as I can see the square edges of the presser foot making imprints around the lid as I work.
Very frustrating, after taking the time to make the jig, to have such an unpleasant result. Help appreciated.