Have a look at this wacky machine that claims to be able to produce methanol from air or exhaust gas in a single step, cheaper than current production methods, if you just feed it electricity:
It does need an enormous amount of electricity, but far less than existing synthetic e-fuel production methods. They also have a design for a giant version of their machine that they say should be able to remove 1 gigaton of CO2 from the atmosphere per year in the process of making methanol. Just 40 of those machines could extract enough CO2 from the atmosphere to offset global fossil CO2 emissions 
So it's even more interesting as a DAC carbon sequestration system than as an e-fuel factory.
