OK,
@Sus7 ,
@Liko ,
@TDBASSMAN86 , and
@Plutonium244 : I think I've got it. Been googling capacitors for about an hour so I'm no expert but pretty certain.
The passive tone cap on older passive P and J basses is a .047 uFd. The passive tone capacitor in the Sire preamp is .022 uFd (it is marked 2A223J, and the 223 means .022uFd, it's the square pillow-shaped forest green component standing nearest the volume/passive tone stack on the circuit board), which yields pretty much the effect you're seeing -- only rolls off the very highest highs and leaves a lot of mids in there. Changing that capacitor out to a .047 uFd should give the response you expect -- bright at one end, smoothly dropping to a dull thud at the other --
in passive mode.
(I did this mod myself on a Squier Affinity Jazz after discovering that it came with a .028 cap which didn't cut the tone much; the .047 made it like I expected.)
Whereas I have a spare Sire preamp on a V-style plate, and whereas I may be the world's worst solderer and don't want to ruin the board, I plan to take my 1st Gen V7 to my repair guy and have him change out that .022 for a .047. Then we will find out (a) how it behaves in passive mode, and (2) whether it plays nice with the rest of the preamp
in active mode.
Wish me luck! I will report back in a week or so when I get the bass back.