What is the best way to desolder epoxied surface mount components without damaging the pad? I have tried using hot tweezers at 400C, but the epoxy never melts. It is the epoxy under each small component, not over several components.
If you can figure out what type of epoxy it is, an appropriate chemical solvent might work. For some epoxies, you can find good removers that preserve the stuff under, but it depends a lot on the epoxy used. E.g. this remover can even preserve biological samples, but it's for the epoxy used in electron microscopy. More aggressive, general purpose removers like methylene chloride or "Circa 1867" paint stripper will also damage electronic components and the board.
Epoxy resins are not very resistant to steam or hot water. They absorb it, and then the polymer network is disrupted by hydrolysis.
Since most electronics will not be damaged by prolonged heating to 100°C, and certainly not all will be harmed by immersion in water, the gentlest method (if the components will allow it) would seem to be to boil the PCB in water for between about half an hour and several hours. This should soften the epoxy enough for it to be removed. Doing this under pressure (e.g. in a pressure cooker) will be even more effective. Be aware that the PCB itself is probably made of epoxy resin, so don't try this on PCBs without solder mask.
If you have a source of copious hot steam, like a steam cleaner, this will also work, and avoids the need to immerse the entire PCB.