Re: No way to get solar energy by then...
"some time in the next billion years or so I think we'll just move to a different neighborhood."
The problem is getting to a different neighbourhood, even if it is just a stepping stone to further "planetary systems" that orbit hopefully newer stars.
The nearest star (outside the Solar System) is about 4.3 light years away and given we cannot go faster that the SOL, (we cannot even get close to a tenth, a hundredth, a thousandth of SOL**), so journeying to the nearest star is probably beyond human capability and will be for a considerable time. And if there are no "stopping off points between the Sun and Alpha Centauri system, then humans cannot play "leap-frog" from planet to planet.
SOL is 299,792 km/second.
Earths fastest spaceship, the Parker Solar Probe, has now achieved a speed of 532,000 km/h or about 148 km/second - which is 2028 times SLOWER than SOL.
So, to get to the nearest Alpha Centauri system, using a similar craft, would take more than 2,028 times longer than if we could travel at the SOL - so, it would take about 8,723 years.
Hopefully, in future eons, homo-superior can bend space/time or develop some form of tech to get closer to the SOL....but it'll be long after I and any fellow readers of this august website have passed on :-(