I do exactly the same as Brian. The correct instrument head countersunk 4BA screws are readily available in the UKfrom model engineers' suppliers, & I also use solder paint as it is so much easier than trying to use a soldering iron the old fashioned way. Do not use silver solder, you only need soft solder. Make sure the two mating surfaces are clean & apply the solder paint. (As well as this I tin the screw threads). Heat until the surfaces go molten & then wipe off the brown impurities/flux which form on top, & you will have two nicely tinned surfaces (body side wall & rear face of pad). Mate them together, applying heat & tightening screws as described by Brian, & it should be fine.
In fact, if we get a chance to meet up I'll give you ample solder paint & screws to do the job.