I also own one of those GWB35, and here's my story...
roundwound strings are really rude to the fretboard, so I use flatwounds (d'addario or ernie ball). the sound is a bit darker this way, but I think it should be, as the overall sound of the bass was a bit on the bright side.
acoustically - it's a bit weak, strings do not vibrate for more than 30sec at best. and the sound looses the punch very fast. I think the bridge is to blame - maybe mine is the black sheep (wait, it IS black), but the part where you hook up strings is not aligned to the body, although all of the screws are tight. it's actually a bit bent, equally with all strings, you could put a piece of paper underneath. I would replace it in a hartbeat, if I knew for sure that it would improve the sound.
my experience with the neck is "not so stable" - when I tune it, I need to let go of the tuning machine and not touch the neck in any way, it's that touchy. but it stays in tune well and other than 2 setups a year (1/8th of the turn for the truss rod) requires nothing more.
oh, the ramp - thank you, gary willis. 20min on this thing already improved my playing. it really helps preventing digging in, i.e. you learn to aim your energy into the string completely.
and now we come to the pickup and electronics - worst part of the bass, as many of you already mentioned. well, in search for fatter tone I installed flatwounds first. then, after some time, the onboard EQ began bothering me. so I replaced the opamp on it - TL062. I was recommended a TLE 2022. the result is - output is the same, but dynamics are a bit improved, and the hiss is gone. even with the treble cranked, there's hardly any. the bass control is not muddy anymore - before it just made something along WOOOOO to the sound, now it does what it's supposed to do. price? well, the new opamp costs about 10x as much as the old one, which goes for half a buck, I guess. plus the soldering, which I performed myself. be careful, it's surface mounted - do not attempt to do it if you are not really experienced in soldering.
the pickup was replaced with the custom wound stingray-wanna-be humbucker (wired in series). the dynamics improved vastly, so did the frequency spectrum. will put passive controls in it on monday, just to see the difference (250k instead of 500k for volume, treble bleed mod).