A few things.
1. Differential transmitters and receivers don't magically absolve you of the fact that you still have two, mostly independent transmission lines going over a (presumably dirty) board.
You still have the transmission line behavior of each trace. Differential only works when the behaviors are matched, i.e., equal lengths from transmitter to noise sources (e.g., slot in ground plane) to receiver.
2. LVDS transmitters have a modest common mode resistance. They aren't specified in this way (instead, they are described as pure current sources, a lie*), but it seems to be the case. This will dampen common mode resonances, although not too well because of the mismatch.
*A sufficiently high resistance, in comparison to whatever impedance matters (in this case, the common mode impedance), looks constant-currenty. It may be they are using that approximation, rather than outright lying.
In general, expect an LVDS pair to experience resonant common mode voltage at both ends. The multiplication factor is the Q of that resonance, which can be quite unfavorable (probably less than 10x, but more than 1x). This should be damped by terminating the common mode at one or both ends, but alas that is never recommended (possibly because the termination voltage is almost never going to match the common mode voltage the transmitter produces, and therefore it radiates every time the transmitter goes from Hi-Z to active; that could be addressed by terminating with an R+C, which charges to the transmitter's common mode level without drawing DC).
3. Wait, this isn't on a PCB, or over short distances? And it's only ~10Mb?
Use RS-485 transceivers! End of thread!
If you absolutely must, consider:
- LVDS bus driver (7mA)
- HDMI PHY or something along those lines (CML, basically LVDS; made for driving cables)
- Ethernet (an awfully heavy-weight step up, but will blast through any distance of UTP you hang off of it!)
You are quite correct that the signal needs to be grounded and shielded. STP isn't bad for this, and 15' is probably not at all unreasonable. Ground the shield to circuit ground at both ends. I don't care what you call it, it's got to be RF-bypassed to the circuit ground plane, whatever that is.
If chassis GND is very close to DGND, then grounding the shield to chassis can be acceptable. If not, you are making things very, very much worse, injecting exactly that common mode noise into the receiver!
Tim