In terms of techniques when rolling in ne-waza with a BJJ practitioner, an aikido person should perfect wrist locks from various positions on the ground. Although wrist locks are allowed in BJJ, they are rarely taught, so an aikido person has a comparative advantage when using wrist locks on the ground. However, just like when standing up, tai-sabaki is very important, so too is being able to move your body correctly when on the ground. To do this requires regular practice of ne-waza randori with partners at various skill levels.
Wrist locks can work and I do them when they are appropriate in BJJ. However, you ending caveat about "moving your body correctly on the ground" is the most important. That is, learn BJJ if you want to defeat a BJJer on the ground, which is all about moving your body correctly on the ground. Oh the dilemma!