The Full Shred Neck would be a viable candidate from Duncan. Some guys like the Screamin' Demon. I'm not one of them, though.
He wants something full but with less bass than a Jazz.
I'll say it straight away: I am not a fan of the Jazz Neck for high gain (or the Screamin' Demon, for that matter) because it doesn't have enough push in the upper mids; that is my bias. It is that bias from which I've interpreted his post, rightly or wrongly. Unlike the Jazz Neck, the JB has plenty of push in the upper mid region, especially with a high value pot (500k or 1M) and no tone control. Even with 250k pots the JB has more of this relative to the bass than the Jazz; and relative is all that really matters once it is combined with a bridge with greater output without an emphasis on highs as seems to be the case with the Invader, unless I'm mistaken: I wouldn't own one.
If the JB doesn't work I'd look at offerings from DiMarzio such as the
Evolution Neck or
FRED.