Difficulty in calculating output impedance for the emitter follower
Of course, there is another way - for my opinion, much simpler. My recommendation is to recalculate the procedure you would apply during measurements.


At first, forget for the moment RE and calculate - as a first step - the input resistance at the emitter node. Because the Resistor RB is in series to the base we can take into account this resustor RB at the end. 
Hence, we simply have the dynamic resistance between B and E as seen from the emitter (Ohm`s law): r,e=v,be/ie.
If we set ie=(hfe+1)*ib and v,be/ib=hie we arrive at r,e=hie/(hfe+1).
Setting (hfe+1)=hfe we have r,e=hie/hfe=1/gm (gm:transconductance)
This expression is, of course, identical to the common-base input resistance.
Final step: The desired overall input resistance for the common-collector stge is r,in,cc=(r,e+RB)||RE. 
The resistor r,e=1/gm is nothing else than r,e=Vt/Ic (Vt:temperature voltage, Ic:DC current) 
Comment: The above derivation applies for the case that no signal source is connected to the base coupling capacitor. If a signal source is connected with an internal source resistance Rs we have to replace in the given formula RB by the parallel combination RB||Rs.