To be honest the SRH500 probably has the same neck as the rest of them. The SRs are all basically built around those neck dimensions, I mean when you move to the more expensive ones you get multi laminate, titanium bars and better machineheads, but the dimensions are all the same and overall the feel is the same. Even the SRC6 has a familiar feel to it, closer to an SR bass than an SA or RG guitar neck.
Having just bought the most expensive bass I have ever had, I know what you mean about the instrument rather than the music, but there is something when playing alone that inspires you with certain instruments. And yes, I wouldn't take it down the dog and duck, but I would take it to an open air event, or anywhere with a stage.
When it comes down to it, my Ibanez 1605 is the one that always stays with me. Its good enough to have all the fancy stuff like the titanium, the nord pickups and the burl, cheap enough not to worry about and non shiney enough to not worry about scratching.