In addition to the denotation of "I want nothing else", just want often has the implication or connotation that what is wanted is not a big deal, or is not a cause for concern, etc. There can be, indeed, a sort of diminishing involved.
I just wanted to drop by your new cubicle and say hello.
I just wanted to take a minute to go over these numbers.
I just wanted to take a peek at her sleeping. I wasn't going to wake the baby.
That's probably not the meaning in the context of "the gift of Salvation" :-)
But sometimes just want carries the implication of "it is only fitting and proper" or that what is being said is heartfelt, that the speaker is expressing humility or deference. That is where the diminishing comes into the picture.
I just wanted to say thank you for all the help and support you've given us during this difficult time.
Humility is most likely the intended connotation in your sentences, thanking God for the gift of salvation or asking for grace.
If we had to paraphrase it woodenly, imagining God as CEO:
We won't take up any more of your valuable time, God, than is necessary to do one thing, namely, express our gratitude for salvation.