Cool research. If you want to be serious about knowing if the changes you make are truly audible and not a placebo effect you should be performing ABX tests:
http://wiki.hydrogenaudio.org/index.php?title=ABXIt may sound silly if you have never been exposed to it but the brain plays surprising tricks on you, especially when you start to think of audio with warm nostalgic feelings - you perceive it that way even if it isn't.
In what you have done so far you can try to ABX the non-linear vs. linear response to see if you can confidently hear a difference.
If you get Paula better emulated via crude resampling/etc. then you probably want to ABX against what you do in software and an actual recording of the Paula, ensuring they are level matched and time aligned. Heck if you can get that close you could just start to compare the recorded audio files directly to check for bit differences to see how close you are.
I'm not a Paula guru, but I would also suspect it is the crude and noisy/aliasing resampling + 8-bit that provides most of the distinctiveness of the output you hear, not so much the non-linearity.
