What mechanisms might make a substance travel different distances on the same TLC plate?
are there other reasons why the components of a mixture should have different Rf values when spotted separately?


One might speculate that two polar reactants form a less polar "adduct". This should however result in an additional spot, rather than in altered $\mathrm{R_f}$ values for the individual compounds.

But this is speculation. Admittedly, I have never used the cross spot method. Neither have I ever observed that spots of the reactants had different $\mathrm{R_f}$ values in the reaction mixture.  

On a side note: What always worked for me was:


Don't apply spots but bands and overlap them.
"Sharpen" the bands on the base line by developping the TLC in methanol or another polar solvent first. 


Together, these two tricks allow to destinguish between two compounds with very similar  $\mathrm{R_f}$ values.