Both songs express disappointment & disenchantment with life, and a longing for death.
In Trying to get to Heaven Before the close the door, they seem to be cross pressured. Trying to get to heaven expresses a belief in the transcendent. Before they close the door expresses doubt. It seems to say he wants to get to heaven before he loses his faith it exist.
Not Dark Yet doesn't seem so cross pressured. With the second part of the phrase, but it's getting there, I get a sense that he sees death as the end. Dark, nothing else.
Prof Langguth has referenced the song "IS That All There Is?" It also has the theme of disappointment & disenchantment with life, however there is no longing for death. The last verse states: I know what you must be saying to yourselves. If that's the way she feels about it why doesn't she just end it all? Oh, no, not me. I'm in no hurry for that final disappointment.
Here is a link to that song: "Is That All There Is" by Peggy Lee