I was told this morning by Oystercard that advance renewals are only
online and not via the machines. I hope he was wrong. He didn't sound
that confident about anything he told me. (Especially when I asked "this
IS going to get better soon, isn't it?")

This is true. The machines can only renew Oystercards to commence on that
day ...

Not in my experience. Can't remember whether I used one of the standard
touch screens or one of the quick ticket machines (possibly the latter).
Worked fine renewing in advance.