The EBMM SR5 and Sterling 5 are different enough from the Stingray 4 that I would give them some serious thought. They can get a similar sound to what you're used to, but with the 3-way switch and a little EQ, they can do a lot more, IMO. I'm less a fan of the HH/HS versions of those, but those are very nice, too.
Another serious contender, and one of my personal favorites, is the EBMM Bongo 5. I have an HH, but I wouldn't mind an HS. Or better (for me), a fretless HS w/Piezo. Sure, they can do a "Stingray-esque" vibe, but they definitely don't stop there (or even start there, really). Very versatile, and far warmer than I first imagined it would be before I tried one. With everything flat, it sounds warm and clear - very supportive, and a great fit in rock/pop/country/blues scenarios. The 4-band EQ can do just about anything, though. I often get a pretty close "Pbass" approximation with the front pickup and some EQ adjustments. Close enough for rock'n roll, anyway. If I need closer, I pull out my Pbass. Of course, if you're after a Jazz bass, the Bongo isn't gonna do it, but it's very usable bass with an excellent feel and nearly perfect balance and great tone, with a B-string as good as anything out there.
Right behind, or maybe parallel to the Bongo, is a G&L L2500 with the "K-switch" option (single coils). That is an altogether different animal, but fabulous quality, fit, finish, and TONE. G&L also offers the M2500, with slightly more modern pickups and a more conventional 3band EQ. Since you're also interested in a Jazz 5, they have the MJ5, which is basically the same bass as the M2500 with a Jazz-style pickup. Not single coil, but a linear 'bucker like Sadowsky and others use.