I tried the above answer using:

rownames(mat.z)[row_order(ht)]

Error in rownames(mat.z)[row_order(ht)] : 
  invalid subscript type 'list'

And got this error so instead I did:

ht <- draw(ht)
order <- row_order(ht)
order_unlist <- unlist(order)
rownames(mat.z)[order_unlist]