I would try ATF (automatic transmission fluid)
Has worked pretty well at rejuvinating plastics and rubber for me. Basically it has additive packs to condition seals that also work to nourish the rubber.
You can get some of the "stop leak" type automotive fluids that are basically designed to swell seals, but they might over soften them.
Try the ATF and see how it works out, then experiment with the "stop leak" if it doesn't get you there.