For the soldering-
Radio Shack sells very fine diameter (maybe as fine as a 64th) that is 2% silver, and is quite strong.
Due to the tiny diameter, MAPP is not required. I use Acetylene with a small tip. A soldering iron just doesn't have the "juice", and will result in a cold joint.
Flux both the screw head, and the basic location for it on the back of the inlay.
Heat it up (maybe 5-7 seconds) until the flux flows. Pull the torch away (important step!), then set the solder on the flux. It might stick a little, or just sit there not melting. PERFECT.
Now, take the torch back into action, and the solder will melt into a little dollop. If you try to put the solder down initially with the torch blowing, the gas pressure will always push it away, and you will never get it where you want it.
Put the roll of solder aside, and with a small flat blade screwdriver, smear the solder into a thin film (heat is on it with the flame).
It will tin perfectly every time.
Repeat the process for the screw.
Apply flux again to both tinned surfaces.
Set the screw where you want it, apply light pressure (just to hold it, and to prevent it getting blown away), and heat it until it re-flows.
Takes a few seconds, and makes a mechanical joint for retention if you decide to forego little brass nails.