I think any Aikido response to this should be to avoid getting to the point where the choke is already set and being applied.
The body slam option is a great one, I've seen that shown in commando training manuals even.
Due to the close bond between our Aikido and Judo we tend to respond to any sort of choke/strangle attack by nailing our chin to our chest (to protect the neck by using the chin and jaw line) and by tai sabaki (body movement) to break the attacker's balance.
A skilled bjj/judo player would be somewhat resistant or expecting a balance break so my next movement would be to apply atemi to the nuts (ridge of hand, up and in @ 45 degrees) with the inside hand while using the other hand to push the attacker's face/head up and over (sokumen irimi nage style). Depending on how effective my initial atemi was, I may have to use something like pressing the point of the thumb into the angle of the aggressor's cheekbone while pushing over.
Alternatively to the ridge hand to the nuts, grasping a handfull of skin on the inner thigh and twisting also causes uke to react by raising his leg, hence floating his weight upward and assisting the subsequent push of the face/head.
After pushing the head, move in with a deep irimi (tsugi ashi) and keep the back straight so uke does not bring you into the ground with him.
Chances are uke will let go of your neck by this time to avoid splattering his own brains on the ground.
Will try to give pictures to describe this, I've yet to see this variation of gyaku gamae ate (sokumen irimi nage for trad. aikido folks) countered when done properly.
The best thing though, is to avoid getting trapped from the outset. Be aware.