To start, Myne's 'main reason' for saving them essentially come down to "I can't read book in peace after seeing THAT and knowing they're there"
So the answer Lutz helped her come up with is essentially to teach them how to survive by themselves by have them run a paper-making/printing workshop:
1. To reduce the food necessary, have them go foraging (that's the main excuse, the real reason is for gathering materials for the workshop)
2. The workshop's earnings will be used to buy supplies for the orphanage, especially for winter preparation that need a lot of fund in a short time.
2.1 In winter where they can't make papers, the workshop will simply do winter handicrafts (started out as one of Myne's whim as usual, basically teaching toys for children)
3. Teach them how to cook so they can ensure some amount of food for the children (at the same time it's also an excuse for her to have a chef she can train for Italian Restaurant)
She also plan to clean up the basement.
Of course she need to talk to Head Priest first, who helps her ensure her ideas can be implemented without causing issues.
For #1, she was going to just make EVERYONE in the orphanage her attendants, so she can officially order them to go foraging (like how Fran and Gil can go outside, but not others)
Head Priest tell her if she do that then other blue priests can't get new attendants and that's a problem, instead she can simply order them on errand in her capacity as the orphanage director.
Lutz, Tuuli, her dad, etc will be in charge of their first few trips and to teach them the rope.
#2 - He is fine with it but he'd like detailed reports about it.
#3 - He said it's natural for her to have exclusive chefs (and other specialists) so bringing in cooks is fine.
And for cleaning the basement, they can order the orphanage to do it under the guise of welcoming the new director.
So she did, and basically start one of the early 'legends' of the Saintess.
Btw, after Myne saved the orphanage, Delia had a...'tsundere' fit? of "why, why couldn't you have come earlier, to save me earlier" and Myne just pat her head and promise the next time she's in trouble, Myne will come save her.
And a lot later on.
Head Priest "wait, the children at your orphanage can read, write, calculate before baptism AND your grey priestesses know your food recipes?"
Myne "DAS RIGHT" *smug* "My people are special, so if any noble want to buy it's not going to be cheap"