I will probably wrap the PCB with my old seat foam!I just put it in a plastic bag with a window to read the odometer and the servicing module lights. It would be a good idea to chuck in some of those dampness-absorbing sachets.
Soldering to the back of the bulb connectors should work. Just try to make sure that you use similar wattage bulbs, or you can do what I did for some of mine, and use a 5v LED with a 470 ohm in-series resistor.
I have tiny 12v LED lamps which are around 0.1 watt, so don't think there will be an issue. The BMW warning bulbs are all 1.2 Watts from what I have seen.