Seriously, I wish I could agree with your statement that continuous acceleration of 1 gravity for the duration of a trip to a nearby star was within our technical grasp.
It is not.
If you call for continuous acceleration for the entire trip, our options are various extremely low-acceleration reaction mass drives (electric, ion, etc.) or light sails. Either will take multiple generations to reach even the nearest star.
And if you *don't* insist on continuous acceleration, but instead call for a boost, drift and deceleration phases, it will also take generations.
The Alcubierre Drive sounds very nice, but it's not within our technological grasp. It's not even certain that the physics behind the idea are sound.
As for maintaining 1G for years, as opposed to minutes, we have no technology that can do that. None whatsoever. Further, it's by no means certain that we will ever develop that technology. It's a very, very speculative proposition.