This might be a completely dumb idea and it must've been explored before, but how about attaching the antenna to a string and trailing it behind the ship at a considerable distance to clear the extent of the plasma shield. Is it that no string is strong or plasma-resistant enough?
They mention this in the article, where they talk about extending an aerial out past the plasma sheath. They then say "this allows communication until the aerial ablates."
I think the plasma forms a complete enclosure, i.e. there is no "break" in its surface at the tail of the spacecraft. The pole will need to cross the surface of the plasma shield meaning an exposure to very high temperatures. OTOH the pole can be insulated the same way the front of the craft is. It looks doable in principle, so I wonder what other problems are there.
Could it be that extending the pole during the descent makes the design of the hull more complex and through that more fragile?
It would seem to me that any antenna that extends outside the 'plasma bubble' would still be traveling at the same speeds and subject to the same problems as the shuttle.
