My theory is that Murphy -- by declining to take up an offered Sword -- has become eligible to be "drafted" by the All-Father to become an Einherjar. But she's also got her Catholic stuff, so it's not like she is "all-in" and 100% committed.
Remember how Harry's GS experience was a bit of a "con-job" -- Papa Murphy kinda-sorta hinted at consequences if he didn't do it; but later on, Harry figures that Murphy most likely hadn't fooled Uriel at all, so ultimately Uriel was running the con... culminating in the con where Uriel sends Harry back, when Harry chose to pursue "what comes next."
I think Murphy is going to have something similar. "Well," says Gard. "You certainly could go join the White God up in Heaven, you've earned your Final Reward. But my own patron favors a very... active... afterlife. Dare I even say -- when the need occurs -- a combative one. You might think of it as a lateral transfer." Murphy wants to keep fighting, keep protecting people, keep being Harry's backup, and absolutely does not want to retire to join the Heavenly Choir. So she likes this, and pursues it.
Then Murphy discovers that whole "living memory" clause, and goes "fuck that."
And she starts looking for ways to bend and break the rules, and come back sooner...
... which is precisely what Uriel wants from Murphy.