You are correct; you won't be able to do anything about it. A major, completely insurmountable, problem with audio is that there's never going to be an 'undistort' plugin - because for one to exist, you'd need a 'correct' reference point for what you want to do, and by definition, that doesn't exist. Declipping works by looking at the rates of change of individual peaks and estimating where they would have stopped if the system didn't overload, and only has a very limited range of working.
Having said that, in your case you could try one thing and see if it makes any difference, and that is to normalize the offending audio to 0dB (the point where it would be deemed to be clipping) and then run the declipper. This should fool the system into treating all the points where the signal hits 0dB as clips, which they wouldn't be if they were lower in level. Personally I don't think this is going to make much, if any, difference because most of the distortion you will have has come from reproducing your signal from laptop speakers, instead of recording the feed directly. If you want an easy way to record the incoming signal you could use something like SoundTap, which will extract it from the incoming feed and record it directly. I've used it for ages, and it's pretty good at what it does - easy to set up, easy to run and you can dump the files straight into Audition to edit. Reduces the problems with this sort of issue a lot, and it will also record anything else that's streamed.
SoundTap (my only involvement is as a satisfied customer)