Moya was always on the move...in the same general area of the Galaxy where the Scarrans and Peacekeepers were always around the corner.
Voyager's problem was that if they did have such a recurring antagonist you'd need to explain why they weren't assimilated by the Borg long ago. Which is another problem with the Delta Quadrant setting, the ever present threat of the Borg would mean there couldn't be any big civilizations/antagonists that could be that spread out.
Unless you make them powerful enough to fight off the Borg, which means they'd still be too powerful for Voyager.
Voyager's problem was that if they did have such a recurring antagonist you'd need to explain why they weren't assimilated by the Borg long ago. Which is another problem with the Delta Quadrant setting, the ever present threat of the Borg would mean there couldn't be any big civilizations/antagonists that could be that spread out.
Unless you make them powerful enough to fight off the Borg, which means they'd still be too powerful for Voyager.