Combined RF and baseband noise simulation in LT Spice?
In other LTSpice simulations I've simulated the demodulation
accurately in the time domain. What are suggestions for a way to
perform this frequency shift operation within the noise simulation
which is based in in the frequency domain?

This is a common problem, the noise needs to be modeled but its dependent on other things in the circuit.
If preforming a .noise simulation, then frequency effects don't mean much because only the Vin vs Vout the gains and noise added from resistors is calculated. The gains are similar to an .ac analysis. So a .noise analysis is more like a .ac analysis but with noise sources added from components and amplifiers.
If the noise simulation you want to preform depends on time then it may be best to simulate noise in a transient simulation, this can be difficult with complex circuits as you need to add a noise source to the noise sources that matter (usually the largest ones, or noise sources before amplifiers, noise adds by the sum of the squares so very small noise sources do not contribute and need not be modeled)