Hi Robert,
It appears as though the Xs are marking places where the parts cross – in the first example, the baritone sings below the bass at the Xs. In the second, the tenor sings below the lead.
How you transcribe that is up to you – but I would probably place the x as a word-sign expression before each note above which it is printed. Unless it’s indicated in the score that that’s exactly what the Xs are there for, you don’t have to explain them. But do put in a TN saying how you are transcribing the Xs.
Kathleen