Your recording sounds fantastic to me.
It's true that thicker strings have partials that aren't exactly harmonic. Ideally they'd be exact multiples of the fundamental frequency, but they actually end up a little sharper than that, and that difference is bigger the stiffer the string. You hear about this more with pianos (google "piano stretch tuning") which have a huge range (the lowest note is the same as the low A on a drop-tuned 5-string) and have very stiff bass strings. The bass strings on a piano are tuned so that they're a little flat; my understanding is that otherwise if you played left-hand octaves, for example, they'd clash with themselves. I wonder if "stretch tuning" would make any sense on a bass? If you tune the E string down a bit, does it make those octaves sound better to you?
I'm not hearing it on your recording, but I probably don't know how to listen for string inharmonicity. I wonder whether maybe you just need some time to get used to the sound of the new strings?
Yeah, It's only been 4 days since I installed it on my bass, I guess I'll have to get used to it, it might drive me nuts a bit