re: Some real world modifications would be needed, but it is a very workable design.
And we'll have to incoproate engines that can move the Eagles at FTL speeds, which is what they were somehow able to do as the Moon itself was hurtling through the galaxy at FTL speeds (after the lunar farside erupted form numerous nuclear explosions from all the waste dumps there, kicking the Moon out of its orbit around Earth and on into deep space), yet the Eagles were often able to leave the Moon, explore an alien world, have a few extras get killed, and return to Moonbase Alpha.
And the crew and colonists will need 70s haircuts and outfits, complete with bellbottoms. FTL engines may be easier to deal with.