Salvation is a continuing process, though. We don’t adhere to once saved always saved. So, should we not pray while in a state of mortal sin or should we be closer to being a saint on earth before praying for others?

Uhhhh… I think you misunderstood what I said. I didn’t say anything about the mechanics behind salvation, nor the ‘once saved always saved doctrine’, nor moral sin, nor the saints.
I’ll clarify my point by commentating on St. Alphonsus de Liguori’s message.
You have but
One soul to save,
One God to love and to serve,
One eternity to expect.
Death will come soon,
Judgment will follow and then
Heaven or Hell forever!
Therefore, O Child of Jesus and Mary,
Avoid sin and all dangerous occasions of sin.
Pray without ceasing.
Go frequently to Confession and to Holy Communion.
You have but
One soul to save,
One God to love and to serve,
One eternity to expect.
I interpreted this part of the message to mean that we should look after ourselves first and foremost.
You seemed to have taken it literally, DZ. We of course must strive to save others, but we can’t help save others without first helping ourselves, making sure that we as individuals are pleasing in the eyes of God.
If a person strives to save others without first attempting to save himself, then he, either willingly or unwillingly, adapts a hypocritical mindset.
Death will come soon,
Judgment will follow and then
Heaven or Hell forever!
Therefore, O Child of Jesus and Mary,
Avoid sin and all dangerous occasions of sin.
Pray without ceasing.
Go frequently to Confession and to Holy Communion.
In order to save ourselves and others, we must follow the above advice.
If one deliberately skips confession, a most fruitful form of penance, without just cause, he is damming himself. Can a person on the road to Hell save others? He must first save himself, yes? Hence the context of the 1st stanza.
Conclusion: We of course must care about others, but we must provide for our own needs first.
Don’t take the 1st paragraph too literally. the Saint isn’t saying that we can’t help save other souls while on Earth. He’s only emphasizing the importance of maintaining the holy state of our personal souls.