Conceptually, what is the Message frequencies affect on the FM signals rest frequency
I think you are confusing your signal frequency with your signal envelope. FM radios adjust the frequency by the envelope not the frequency of the signal. 

\$F_{FM} = F_R + F_{D}*V_{signal}/VMAX_{signal}\$

The rest frequency will stay the same.

However, if your signal has a dc component, it may appear to the receiver that the rest frequency is something different.