Good question and I wish I had a good answer for you. I’ll tell you of some of my experiences in dealing with folks who get cramps. The first time I really encountered a chronic cramper was with Mark Twight 15 years ago. He was convinced that it was some sort of nutrient imbalance. In his case he cramped during prolonged/endurance type activities. His cramps finally resolved when he began to train aerobically and improved his endurance. I have had one other very similar experience with a good athlete with poor aerobic conditioning who cramped during prolonged exercise. His cramping also went away when he became aerobically more fit.
Your case sounds different in that yours occurs during strength training. While there is much debate surrounding the cause of cramps we do know what they are: The actin and myosin cross bridges fail to release so that the muscle can’t return to its normal length. What makes the muscle go into a spasm then? Maybe there is some sort of positive feedback loop that the nerves and muscles get stuck in that causes increasing recruitment and subsequent cross bridge rigor? I’m not sure. But we do know that when the muscle’s ATP stores are depleted the cross bridging effect fails. This is what happens when you see muscle failure in strength exercises. All this could be related.
The killer core bridge puts a big load on the hams for sure and if you are getting cramps when you do this or any other exercise then stop NOW. Find a more mild way to engage your hams because you are clearly overloading them.
I suggest doing some hamstring conditioning. You have a medical problem and you can not proceed with this type of training until you resolve that medial issue. Find some mellow exercises like supine bridge where you lie on your back, knees raised, then lift hips from floor while leaving shoulders on floor. If you can do this successfully with no cramps 4×20 reps 3x/week then raise one foot off floor to increase resistance.
As a general rule find some hamstring strengthening exercise you CAN do without cramps and use that as your starting point to build toward these harder exercise.
I hope this helps.