Speakers: don't know the min. distance depends on the size of the magnets really. My Gorf cab which I'm trying to resurect (KRK hasn't returned a message in a while) has plain speakers mounted underneath the bezel. You could try the car speakers and just watch for problems. I warped a screen on one of my pc's years ago, but a few days after moving the speakers the screen reverted and was ok. I don't think most pc speakers are actually shielded, the magnets are just so small they don't cause problems.
For the soldering: that's the pad I recommended. Strip the case off the pad and peel the rubber buttons off of the board. You'll be able to see all the traces. Under each rubber button will be a circular mesh of traces, kind of like when you almost interlock the fingers of both hands. They'll be close together but not actually touching. One side of this mesh will be the ground, the other the contact. You'll be able to ID the ground as that trace will connect to 1 side of the mesh on every other button on the board. Take a flat blade screwdriver or similar and scrape the green coating off so you can connect to the copper trace. Don't try and solder through the coating. You can solder into this trace anywhere on the board and it will connect to every button. The other side will run directly to the chip mounted at the top of the board.
On the (contact) side of the mesh you'll see a small copper pad w/no coating. The best way to make these connections will be to drill a tiny hole through the center of this pad. Just big enough to slip a piece of solid 24ga or smaller wire through, and solder it to the pad. Then connect your controller to the small jump wire. Almost no voltage passes through this wire, so wire size is not an issue.
An alternate method is to scrape the coating off of the trace and flat solder to the bare patch. This is what I did on my jukebox controller, but only because I was in a hurry and didn't have a small enough bit at the time. You have to be carefull as heating the board as once it's heated, if you pull on the wire it can easily separate from the board and break the connection. If this happens you can try again further upstream of the break, but the traces get pretty tight in some areas. I lifted 4 traces before I finished. Fortunately I only needed 5 buttons at the time so I had plenty of room for do-overs. I'm redoing my control panel and will be using all 12 inputs on another pad, so I'm going to drill and be more carefull.
Once you have this done w/all your jumpers connected to the board I'd recommend taping the sh!t out of it w/electrical tape. This isn't to insulate the connections, but to take any stress off of the actual connections if you pull a wire by accident.
After that run a single ground wire to the common side of all your buttons, and then to the common on the pad. connect each jumper from the pad to a contact on each button. Program each button for it's function and you should be in business. If you mess up and can't use the gamepad, it's only $10 for another go, so that's good. If you mess up 4 times you could have bought an Ipac and not had the problems, so try and limit the mistakes.
Good luck, and as always No warranty offered or implied and your mileage may vary.