I think my solution is lurking in this slide somewhere:

Can we modify \sigma^2 to vary with location of x_i and not be fixed? And maybe allow correlations between y_{1j} and y_{2j} instead of the 0s on off-diagonal blocks?
I think my solution is lurking in this slide somewhere:

Can we modify \sigma^2 to vary with location of x_i and not be fixed? And maybe allow correlations between y_{1j} and y_{2j} instead of the 0s on off-diagonal blocks?