How to Combine / Fuse 2 Least Squares Estimates?
I'm unsure if this is the answer you are looking for, but why not save and share $|H_i|^2$ in addition to the least squares estimates?

If you have $w_1^*=\frac 1 {|H_1|^2} H_1^t d_1$, $w_2^*=\frac 1 {|H_2|^2} H_2^t d_2$, and also know $|H_1|^2$ and $|H_2|^2$, you get the total least squares estimate with:

$w^*=\frac 1 {|H_1|^2+|H_2|^2} (H_1^t d_1 + H_2^t d_2)=\frac{|H_1|^2}{|H_1|^2+|H_2|^2}w_1^*+\frac{|H_2|^2}{|H_1|^2+|H_2|^2}w_2^*$.