jaxd, your plant wasn't stretching from lack of light. You cut off its bloom stock, the only one it will ever make. The pups grow on the ends of little strings but they have to root before the mother plant dies. I imagine your old pot didn't have room for them to root and without nourishment from the older plant, they couldn't sustain themselves.
Sempervivums are monocarpic. That means they grow, bloom and die. But, the rosettes growing around the 'skirt' take over and the plant grows. I'm not sure why anyone would core a semp. The plant will die after it blooms whether it sets seeds or not. The plant will die after the bloom stock is initiated, there's no stopping a monocarpic plant from doing its thing.
Put your plants outside in shallow bowls (or on flat rocks- I've never tried this but I'm going to). Don't bother to water unless you have a heatwave. I water mine about once a week in summer but its also 110 degrees F out there.
All that said, the reason Tapla's semps are doing well is that they are outside. Semps are not house plants - they need cold temperatures to do well. Put them outside.