Glad you figured it out.
I'm kinda wondering why your elbow didn't hurt prior to the new stance as you didn't change the way you gripped the cue but I've got a theory.
I'm no Dr. so this really is just a guess but it would be interesting to know if any feel my explanation makes sense.
With the new square stance your elbow is higher at address causing your forearm to be closer to your bicep. Effectively this puts the ligament on the back side of your arm (the one running through your elbow) at almost maximum stretch at address. On impact the forearm almost hits the bicep and that would put the ligament at max stretch. This would become even more problematic for a power shot as you'd almost certainly make contact with forearm and bicep and seriously stretch the ligament. Dropping the elbow is a way to achieve cue power without ever having the forearm and bicep meet but is harder/less natural feeling to do with a square stance. If someone is used to the side on stance, adopting a square stance and dropping the elbow can feel like your leg is in the way. People then stop dropping the elbow on power shots and cause strain on the elbow ligament trying to obtain the power they want.
Loosening your grip has allowed that ligament to be more relaxed at address which is preventing the overstretching. The injury seems similar to the strains one sees if they run without stretching first.