Using an absorptive switch will only help when switched away from the LNA, not when you are connected to the narrow band antenna.
Definitely plot the K-factor, if that is above 1, then you have verified stability in all source/load conditions. Your goal should be stability at all frequencies at any source impedance. This will inevitably take a toll on the noise figure, but this will ensure stability. You could make your life more complicated by characterizing the impedances you expect to be presented to the input of the LNA in all circumstances and design for stability in these regions of the smith chart. Plotting the input and output stability circles on a smith chart is needed in this process, but nothing beats an unconditionally stable LNA when you're faced with the concerns you've described.