AFAICT the only real long term solution is the relief wells they are still drilling and MAYBE completed next month. I hear so many “experts” chiming in and many are pretty skeptical over these temporary caps holding. Some pretty catastrophic scenarios have been posited too that I am not too hopeful near term and long term is simply too hard to predict right now.
For the moment, it seems, the oil has stopped flowing. The cap may start leaking, though. As @Cruiser said, they can’t be sure they can control it until the relief well has been drilled.