Oh, I forgot I did this. Here's a set of examples of pickup recordings with different processing to try to make them sound better. You'll want to follow the link to see all 15 variations, I don't want to post 15 soundcloud players here. None sound as good as a mic, and spot checking I'm not hearing anything to write home about, but maybe you'll get some ideas from it. These are all using the K&K pickup. This was long before ToneDexter, so that isn't one of the examples.
https://soundcloud.com/doug-young/se...-a-pickup-demo