The thought of "prying open the cylinder" just sends shivers up my spine at the damage that could result.
Tip one. If you have a problem don't grab the nearest pry bar, instead use your eyes and look things over closely.
Has the firing pin retracted? If it hasn't, your problem is a pierced primer and simply rocking the cylinder from side to side will usually pop it free. The fix for this is to replace that extended length firing pin with a Factory firing pin or reduce the mainspring energy enough that you don't pierce the primer.
Look at the front of the cylinder. Is one of the bullets projecting out above the front surface of the cylinder? If so that is the cause for your jam. Take a wood dowel and a hammer and GENTLY tap that bullet back into the case so that it's below the front surface of the cylinder. Then open the cylinder and contact Hornady about replacing your defective ammunition. Because a well made 357 Magnum should NOT be jumping the crimp in a revolver as heavy as a 686.
The third issue is a seriously loose ejector rod and you should have noticed problems opening the cylinder LONG before it unscrewed enough to actually "jam" the cylinder. On a 686 this has a LEFT HAND THREAD, so you tighten in by turning it backwards. Anytime a loosened ejector rod is causing problem with opening the cylinder it can be tightened using a thumbnail to "pinch" the knurling and repeatedly cocking and uncocking the hammer to drive the cylinder around. Once the knurling starts grinding down your thumbnail it should be tight enough to allow the cylinder to open properly. Then you should take the revolver home and tighten the ejector rod properly. NOTE, for safeties sake you should shoot off any loaded rounds before any attempt at tightening the ejector rod in the field.