Thanks for the replies! These responses are in line with what I was thinking while lying in bed last night. The output side of the first switch is common to both the feedback network and measurement equipment (ADC, voltmeter, etc)and thus it's resistance is effectively negated and merely affects the output impedance of the op amp. However, if the switch resistance is in the milliohm range while the feedback resistors are in the kOhm+ range, the benefit of going with the circuit in Fig 10 is likely negligible for all but the most accurate of circuits (and then there's probably plenty of other design issues that also would need to be addressed), which exmadscientist pointed out.
The second switch is nothing more than a selection circuit necessity due to the first switch being common to the measurement output and feedback network. The second switch adds to the output impedance to the measurement side, but assuming that the measuring equipment has a high impedance input, the switch's effect is negligible. What I particularly like about this arrangement is that it's much easier to ensure that the switch's contact whetting current is met.
Using a DP3T switch, I can implement a 3 selectable gain circuit as described in Fig 10. If my feedback resistance ends up being sufficiently high, I can use the same switch, but I can switch out both ends of all feedback networks except for the one selected. I don't know for sure, but I suspect this would reduce some of the stray capacitance. Then again, I'm primarily interested in DC, so the "Kelvin switching" is likely more desirable.
I agree that 14 gets a little crazy. There's probably a handful of ways you can arrange your switches for the same outcome, but I suspect there's better ways to minimize stray capacitances.