Had a look on Drifters site this morning - their sister site Westgate Ark have an advertisement similar to yours for a lady looking to rehome her parents cats urgently. I would try them again.
Also, if you were willing to take the cats to one of the rescues there may be a far greater prospect of them agreeing to take them, rather than turning you away by phone, but please only do this if everything else fails - travelling may well stress the cats out.
Helping Pets also use fosterers which is a possibility.