One thing that came to mind is if I use an op-amp, would that essentially kill any voltage left for the ADC to read?
No it would not.
Basically you want to use the op amp as a comparator to trigger a digital input so you know what channel to read. How many of these signals have you got? If you have a lot then you might want to look at a 8-line to 3-line priority encoder 74LS148 to signal to you what sensor needs reading. You can cascade these to have more input lines.
However, whether this will actually solve your root problems is another matter.