Is there a better alternative for on-demand, on-location power generation?

You can use fuel cells; I'm sure external steam reforming based hydrogen (in protein exchange membrane fuel cells) works very well, but I'd not be surprised if some hydrocarbon or alcohol fuel cell beats it in TCO; also I'd expect liquid oxygen to be readily suited to be trucked-in with the fuel they feed these turbines and by the power of a simple dry heat exchanger exchanging between ambient air and combustion "air" they could use exhaust gas recirculation with pure (other than the exhaust gas diluting it so the flame doesn't melt the turbine blades) oxygen which would as a side-effect allow them to condense out water to obtain nearly pure CO2 exhaust. Liquid oxygen is around 100$/ton and you need 3.21 tons of it to burn one ton of methane. If you use kerosene instead you're at about 2.58 tons of oxygen per ton of fuel.

Note that the absence of nitrogen otherwise plentiful in combustion air eliminates NOX formation.

What they do for the oxygen production is they condense air and then distill it; IIRC it's mainly done for steel production where they use it to burn off carbon dissolved in molten iron. It's side product liquid nitrogen and argon are primarily produced from this but are mostly considered side-products of the "oxygen refining".