To be honest I've never heard much natural anything outside of going hifi. I can see why people might call them natural because there is not much exaggerated. They are just too lean in the bass for me to consider them a complete headphone. I think that for the OP these are not complete enough for his needs. I do think the 595/598 have good mids but overall it's simply a 90£ headphone.
The DT770 hooked up to my Fiio E11 was incredible and doesn't totally loose out to my flagship stuff. It's not for everyone though. This is all a preference game I know but it terms of a lean low-end that's a proven fact but some may be fine with it. They also tend then be a bit bright for some but I didn't find it an issue.
I do find the Senns work for competitive play quite well though since having a lean bass makes for extra detail in the other frequencies. But for movies and music you wAnt an all rounder.
I tried the bass boost function and it made them sound daft and artificial.
I don't dislike the 598 but I think it's so overrated it reminds me off the whole M50 craze a bit where it's just recommend with giving a though to what people are looking for. Just my opinion