I acquired a used Stingray a few days ago. It has a Status Graphite neck
Ah ha - is this a factory limited edition or an aftermarket mod - I'm presuming the latter? Anyway I'm glad you've solved your problem.
I've never played a Stingray other than a stock one, and in spite of some people referring to the issue, I've never had this problem. If anyone cares to look, there's currently a post on the Musicman bass forum by a guy called Pertyman - it contains a video of him playing Paul Simon's Graceland on a 1992 Stingray fretless - there is no hint of a weak G string, and all the harmonics and high notes ring out as you would expect.
A serious mistake, IMO, some bassists make when using Stingrays is to put the bass EQ on full (you can't use it like a Fender tone control) - yes it sounds nice on the low strings but it also overpowers your mids by making too scooped a sound - and your higher notes can 'appear' to be less present - however you probably will find the bass is still cutting through the mix out in the room, even if you can't hear it properly, and if recorded, will probably not be a problem.
I have never modified a Stingray or its pole pieces in 35 yrs of playing these basses. The latest ones are no exception - simply the best mass produced bass you can get - you could take off the pickguard if you wish, and the woodwork and finish is perfectly presentable under there ;-)
I do agree on string choice and I think it depends on the bass - the standard EB Slinkies work best for me on my SR4HH; Cobalt Slinkies on my 2 band Classic (although I've re-strung it recently with TI Jazz flats); DR Marcus Miller Fatbeams on my SR5 and Ernie Ball Grp 3 flats on my SR4 fretless. Rotosounds also work well (certainly for a while), as do GHS Flea Boomers. I find 100 to 45 guage work the best (interestingly this is what EBMM ship Stingrays with). I have some Rotosound 95 to 35s on my SR4HH at the moment - they make it sound far more 80s, especially the slap sound, but I'm finding a 35 guage G string FEELS most peculiar - almost like a guitar string.