How do enzymes affect a reaction's equilibrium?
I believe you have misread the first referenced paper. What it says is that the $V_{max}$ and $K_m$ values for the forward and reverse reactions can be varied to optimize a property such as the maximum velocity (represented by $V_{max}$) in one direction, but are always constrained by the fixed value of $K_{eq}$.
The reason that the $K_m$ values (which are pseudo equilibrium constants) can be adjusted is that they represent a reaction in which the enzyme is a reactant. For the substrate, this reaction is approximately $\ce{E + S &lt;=&gt; ES}$.
Likewise, the second paper also describes how the $V_{max}$ for one direction or the other can be maximized, but again subject to the constraint that the respective $K_m$ values must vary such that the overall $K_{eq}$ maintains its fixed value.