We have worked against this type of attack in our dojo. There seem to be a few good defenses, but some depend on mai-ai critically. We have found that IF you have sufficient awareness of the intent and can enter to the side, you can capture an arm in nikkyo and pin to the ground or throw away using the forward motion of the attack. Also, a type of "sacrifice" throw that will work is to fall under the attacker, throwing them over, much in the same way you might continue the motion of someone striking yokomenuchi. The timing again has to be exquisite and nage must not lay there congratulating him or herself but must immediately be up with good zanshin, for all you have done is throw the attacker from a low starting position.
One other technique we have practiced, while not exactly a traditional aikido technique, is to blend with the forward motion and capture the head/throat in a choke. Done well and quickly it can break a windpipe and quickly stop the attack. Must be very very careful practicing this one though. Not for novices.
We have also practiced applying aikido immobilizations from a ground position. It is possible and effective, but not something you normally practice.