About $\zeta(s)=1$. Your "illusion" about zeros close to $\Re(s)=54$ 
well might be caused by working with insufficient precision. Probably
zeta is so close to $1$ your precision believes it is exactly $1$.

Does the "illusion" disappear if you work with more precision?

My results with sage/mpmath:

With precision 16 decimal digits find a lot of zeros close to $\Re(s)=77$.

With precision 40 digits the zeros move to $\Re(s)=82$.

With precision 100 can't find large zeros, only with $\Re(s)<2$.