A quick comment on the flux residue - it doesn't have to be cleaned if it's the water-soluble type. It looks bad but it's harmless.
Brass shim should work for the shields, but make sure it's not too thin or you'll see something akin to microphonics if the flat surface is able to vibrate.
When I worked at Motorola, we had to mould stiff ribs along the surface of the synth VCO covers to prevent issues caused by even the smallest vibrations.
If you have a local junk/surplus store see if they have any cellphones/pagers/radios that you can pull some shields off of.
Just heat the board up with a heat gun and the shields fall off.
As for the battery, I think the ones that came with one, have it sandwiched between the back cover and the PCB. Maybe some can confirm?
