Yari, as always an excellent reply. Good to see you back on here, my friend. Many of the joint locks in aikido that are used to negate a grip or a grab will work just as well from the ground as they will standing. Also, if you talk to many BJJ guys they'll tell you that once on the ground one of the most important things to do is to feel your opponents energy to figure out what he's going to do next. In aikido, feeling the energy of your attacker is extremely important. Transferring that ability to the ground assists you in defending from the ground. As Yari pointed out, though, it depends a great deal on the individual dojo or instructor. In my dojo if, during the course of a defense both parties wind up on the ground they are encouraged to continue with the attack since, in the real world of defense, your attacker wouldn't stop, stand up and reset.
From what I've gathered from your posts the style that really would seem to suit what you're looking for would be the Daito Ryu aikijujutsu that was referred to by Mr. Garrido in another thread. Best of luck to you.