To shield, you need to shield everything fully, so you create a 'Faraday cage' with the smallest gaps in it possible. The shielding all needs to be grounded, or it has almost no affect. Copper on the underside of the pickguard will be grounded by contact with the grounded pots. Run the copper up over the edges of the control/pickup cavities so that it comes into contact with the copper on the underside of the pickguard to ground it.

Whilst you can use copper or aluminium, it's best not to mix the two if possible, as dissimilar metals can corrode each other if they get damp. You won't be dipping the guitar in water, but sweat and humidity could creep in over time and start to eat away at the shielding.

As Colin said, copper tape is cheap and easy to buy.

I'm wondering if you have any of the thick winding of the bottom E string going on to the post (that would definitely make it hard to wind) or whether it's just the thickness of the central core that's doing that. The 0.084"s would be easier to use.

It's not the quality of the tuners that's an issue, as they are pretty decent tuners that come with the kit, but to make it easier, you'd need tuners with a higher gear ratio. You can check the ration on yours, but on a kit tuner I have, it takes 15 turns of the peg to rotate the post once. 15:1 is already pretty good. To make turning the tuner easier, you'd need to go up to 18:1 tuners (16:1 isn't going to be enough of a step to make a difference). You can get 18:1 tuners, but most aren't cheap. You'd get a 20% increase in mechanical advantage using them.

You could probably still get the locking Grover 406Cs at low cost from Pitbull as you've bought the kit, but I'm not sure how well the locking mechanism would grip the thicker bass string cores, especially the low E. The locking pin in the middle of the post is supposed to deform the string into a 'U' shape. If the central core of the string is much thicker than a standard low E, then I don't know how much the pin could deform the string by, and it may slip.

A wider tuning peg would also help, as you get more leverage, but the six-in-line style tuner holes normally haven't got the spacing for larger 3+3 style tuning pegs (you can normally find replacement tuning pegs in different shapes, so you don't have to make up a 6-in-line set from two 3+3 sets). But you could measure the spacing and see if wider tuner pegs would fit.