Both of these pose problems of their own, though.
How can a message be interpreted as being for the Delta Quadrant? If all they have is the direction, then the message might be for the neighboring star or the neighboring galaxy just as well.
And Data specified the Delta location where the Ferengi were stranded as mere 200 ly from the previous spot, which had been in Gamma. The Voyager would have had little reason to graze the quadrant border...
Timo Saloniemi
Voyager had reason to travel in a straight line from the Caretaker's Array to Earth or someplace in the Federation close to Earth. Therefore if the position of
Voyager was plotted on a two dimensional star map of the sky as it looks from Earth the position of
Voyager would change very little from episode to episode and season to season despite getting tens,hundreds, and thousands of light years closer to Earth.
So if the location of the Caretaker Array was 30 degrees away from the border between the Gamma and the Delta Quadrants as seen from Earth,
Voyager would continue to be about 30 degrees away from the border between the Gamma and the Delta Quadrants as seen from Earth for the rest of the series. And thus
Voyager would be a lot more than 200 light years from the Gamma quadrant until sometime after
Voyager passed into the Beta Quadrant and was almost back to Federation Space.
But if the location of the Caretaker Array was 0.01 degrees away from the border between the Gamma and the Delta Quadrants as seen from Earth,
Voyager would continue to be about 0.01 degrees away from the border between the Gamma and the Delta Quadrants as seen from Earth for the rest of the series. And thus
Voyager would start out quite close to the border between the Delta and Gamma Quadrants, and might be less than 200 light years from the Gamma Quadrant early in the series after having traveled only a few thousand light years and while still deep in the Delta Quadrant.
Since Data said the point where the pod of Dr. Arrador was lost was in the Delta Quadrant and also about 200 light years from the Gamma Quadrant, it seems reasonable to deduce that Dr. Arrador's pod was lost in the Delta Quadrant less than 200 light years from the border with the Gamma quadrant. Since Dr. Arrador and his companion were found on a planet that Voyager visited it seems logical to deduce that planet was within the short range of their pod from the point where they were stranded, and thus that
Voyager made its entire straight line journey back to Earth while only a few hundred light years from the border between the Gamma and Delta Quadrants.
The Ferengi may have travelled for a bit before they reached that planet from False Profits..
And how far could the little Ferengi pod travel to reach the planet where they settled? Hundreds or thousands of light years into the Delta Quadrant? Would the pod have enough food and other supplies? Would the pod be fast enough to even travel thousands of light years into the Delta Quadrant in the 6 or 7 years before
Voyager arrived at the planet? And it wouldn't make much difference to where
Voyager started out from unless the Ferengi pod traveled at least a few thousand light years deeper into the Delta Quadrant.
Furthermore, the wandering Delta Quadrant mouth of the Barzan Wormhole did appear quite close to the planet where the Ferenghi settled. If that planet was thousands of light years deeper into the Delta Quadrant than the point where they were stranded, what would be the odds against the wandering Delta Quadrant mouth of the Barzan Wormhole appearing near that planet? Would those odds be well - astronomical?