What are your thoughts about what allows a person to go from spirit prison to paradise? Does it require an ordinance like baptism or is it based only on the person accepting the atonement?
The scriptures tell us that it is faith in Christ (and His atonement) that frees us from the shackles of sin and despair in mortality. I see no reason for it to be any different in the spirit world.
Baptism is necessary to enter the Kingdom of God in both places but I think that Spirit Paradise, while nice, isn’t the Kingdom of God. I think it the place were the righteous have gathered as they wait and work.
Alma’s experience when he converts also appears to run along these lines: (Alma 36:18-20)
18 Now, as my mind caught hold upon this thought, I cried within my heart: O Jesus, thou Son of God, have mercy on me, who am in the gall of bitterness, and am encircled about by the everlasting chains of death.
19 And now, behold, when I thought this, I could remember my pains no more; yea, I was harrowed up by the memory of my sins no more.
20 And oh, what joy, and what marvelous light I did behold; yea, my soul was filled with joy as exceeding as was my pain!
Now is is likely that Alma had already been baptized before this happened. If not, then it seems logical that he would have quickly sought it out. I see no reason for the same to not be happening in the spirit world. When a spirit uses faith to break the chains of sin and if an authoritative baptism awaits them, they would quickly accept it and move forward. If one does not, then getting one would become their focus. They would be forced to wait patiently on the Lord until it happens.