Looking into this more, what I suspect I have to do is to reload the http://wiki.analog.com/resources/tools-software/linux-drivers/iio-adc/axi-adc-hdl module, which is currently statically in the kernel. I haven't studied the source, so what's the chances if I make this a loadable module, loading/unloading dynamically would work?
As for the ad9361_phy driver, I can still change parameter values after loading a new image, so I'm thinking that that driver is still working fine.