I don't feel adequately well read to debate whether they're on course to succeed but a small point of accuracy: only the inertial confinement lot are trying to 'imitate' the sun because they're the only ones using appreciable pressure to trigger fusion. The Tokamak/Stellerator/other magnetic confinement lot are using heat (far hotter than the core of the Sun) to cause sufficiently energetic collisions. In the middle is the Fusor, that's sort of like inertial confinement but not really (apologies for the wooly explanation, it's complicated).
Both have their own reasons for doing what they're doing, inertial confinement is theoretically more efficient while magnetic confinement is theoretically easier to achieve mechanically.
One thought to ponder: we could have fusion power tomorrow and we've had the technology for decades. All that needs to be done is set off a thermonuclear device in a deep hole, pump water down and generate power from the resulting steam. Canakin demonstrated that 5Mt can be contained underground with reasonable effectiveness, though your 'power plant' would have to be a long way from civilisation because it generates quite an earthquake.