I would just buy a new backing plate. I'm also not sure of the spacer/washer you're talking about, but if it is removable and only allows three threads to go into the spindle I wouldn't use it. I have never used a spacer or washer with my PC.
The problem you'll have if you continue to use it is the remaining four threads might give out and this time you might damage your paint. I'd also be concerned about the damaged threads messing up the threads in the spindle, along with metal shavings getting on your paint and buffed in
For about $15 for a new BP I wouldn't want to risk it.