In this case, I don't think solving multiple equations simultaneously is the direction to go, because every row in your table involves two variables: parameter1 and parameter2. And they are different variables from row to row, though they have the same name from equation to equation and you put them under the same column.
For simultaneously solving multiple equations using the suggestions that I gave, equations use the same set of variables from equation to equation. Every variable should have just one value.
What you need to do is to translate what you have done in Excel Macros to JSL, e.g. you need to write a bigger JSL loop to go through every row iteratively.
For solving equation under a nonlinear constraint, one of my suggestions was to convert a constrained problem to an equivalent unconstrained problem. Assume your constraint is an equality, the following example tries to find the solution to y-exp(x)=0, under constraint y==exp(-x). The solution is the intersection of the two curves, which is at (x,y)=(0,1). The minimizing objective is sum of squared errors of the target equation y-exp(x), and the violation of the constraint y-exp(-x)=0. Notice k is a penalty on the violation , and k is rather large.
Also notice, I intentionally put the initial values far away from the solution, and increase MaxIter, just in case you cannot identify initial values that are not close to the solution.
x = 100;
y = 100;
k = 10000;
minFun = Minimize( (y - exp(x))^2 + k*(y - exp(-x))^2, {x, y} , MaxIter(1000));
Eval List( {x, y, minFun} );
show(x, y, y-exp(x),y - exp(-x))
It is a feasible approach if your actual objective can use.