You should use the array of dofs instead of the finite element functions. I think it is not possible to do it with EigenValue(). However it is possible if you use EPSSolve() with PETSc. Then instead of vector= you put array=.
There is an example in
For the case of composite spaces, you can do as real[int,int] Vectab(ndof,nev);
then you put array=Vectab in EPSSolve().
Finally you define
Rh [uu1,uu2];
Lh [aa1,aa2];
for (int i=0;i<nev;i++){
[uu1[],aa1[]]=Vectab(:,i);
//here you can use the eigenvector [uu1,uu2] as you like
//the Lagrange multiplier [aa1,aa2] is useless
}