You also need feedstocks. And a source of CO2. And limits on fossil CO2 emissions. That last pretty much rules out any use of fossil (or methane hydrate) sources and requires you stick to present cycling carbon within the carbon cycle (biomass, atmosphere).
If your time horizon is more than decades to a century or so, feedstocks rules out petroleum (which doesn't make sense anyway), natural gas, or coal.
Conventional non-breeder uranium reactors will suffer from fuel shortages if used for significant amounts of power generation well within a century. Thorium breeders offer a possible alternative, though the technology is unproven. Fusion is even more unproven.
Which leaves solar, wind, wave, and geothermal, all of which have distinctly limited upper bounds, and very considerable infrastructure requirements. Yes, we could get all the energy we need from solar by covering 0.5 - 1% of the Earth's surface with collectors. It's helpful to note that the built environment -- cities, towns, and villages, is on the order of this size. So we're talking about effectively doubling the size of the built environment (though in some cases solar infrastructure can be built over existing structures), with a much more technically complex instance (solar PV arrays, inverters, and power transmission infrastructure are more complex and demanding than ordinary buildings and structures). That's ... a pretty major undertaking, even if we grant ourselves several decades to complete it.
Energy is the problem.
On top of that, Fischer-Tropsch plant and capital are expensive and would take a long time and vast investments (trillions of dollars) to replace the 20 million barrels of oil consumed daily in the US.
Nuclear powered aircraft You're side-stepping your original statement. Producing hydrocarbons at that scale from electricity is unproven. Producing hydrogen might work, and for aircraft (limited in number, limited in servicing points) could prove viable, though with significantly more airframe volume devoted to fuel storage, and with much more complex storage parameters -- most likely LH2 -- than existing fuels.
Solar powered airships I'd suspect that either PV costs would come down, or array designs would be designed to be transferrable between airships, or both. My point was to demonstrate that where solar powered heavier-than-air craft are only just feasible (see the Solar Impulse, with the wingspan of a 747 but just able to carry a pilot), solar-powered airships are highly feasible. Of course, any fuel which would work for an HTA craft would also work for an airship.