Astrobreaking in progress
Kicking a planet sized of mass forward really fast during periastron reduces the companion star's velocity, apastron and orbital period. The loss of mass should be small compared to V Hydrae, so these cannon balls should get fired more and more often until the companion's orbit becomes circular. At that point the firing becomes continuous and the companion drops deeper and deeper into V Hydrae. V Hydrae should become more oblate - more mass pulling it tighter, but more spin provided by the companion.
We will not live long enough to see this happen, but now astronomers know what to look for, they should be able to find similar stars further along the same process.