Plagal is a theoretical term originally used to classify liturgical chants in Western European and colonial traditions, through the mid 17th century. For monophonic chants, plagal means that the ambitus of the melody ranges from a fourth below the final to a fifth above it.
In polyphonic music of the 16th-17th century, if you follow Zarlino's theories, then ...
In my research, I came upon the following
In an authentic mode such as D Dorian, we have octave, here D-D, built
from a lower fifth (D-A) and an upper fourth (A-D), with D as the
"final" or usual note of repose or conclusion.
In a plagal mode such as D Hypodorian, in contrast, we have a mode
built from the fourth below the final (A-D) and the ...
Given the brevity of the melody and the fact that there are no other parts involved, the best way to write it would be as though it were two different songs. That affords the greatest visual clarity and eliminates any uncertainty over whether there are two parts to be sung together or perhaps a main melody and a secondary melody (as opposed to two equal ...
Apart that this song has an up-beat and needs 1 flat it has to be written in 2 versions, because the accompaniment will be different:
I-I-V-I or I-V-V-I.
F F C F 2) F C C F or F Gm C7 F
So you can notate the lyrics with one tune and add the second tune as supplement with the remark that it can be played or sung alternately to the first version.
When just an occasional note is different, a bracketed cue-sized note may be sufficient (example A). In your case, however, I think there are enough differences to warrant an ossia stave (example B). Maybe even a full-sized one, if the two versions are of equal status.
Either way, some explanatory text would be in order, to make it clear that the ossia ...