stray/adoption pull from saved cas sims?

I don't know of any ways to make the game's adoption system pull from the Saved Sims bin. However, there is a way to add the pets from the bin into your household, though it involves a bit of cheating:

1. Go into Edit Town and create a household with 1 adult Sim and the pet(s) that you want.
2. Move the household into town.
3. Press Ctrl + Shift + C to bring up the cheats bar. Type in "testingcheatsenabled true" and press Enter.
4. Go over to the lot that the household from 1. is staying at. Shift-click on the pet(s) and choose "Add to Active Family".
5. The pet(s) should now be part of your household. (ETA: if you want to move the pet(s) to your home lot quickly, take control of them, shift-click on the ground outside your house, and choose "Teleport Me Here".)

If you don't want to keep the adult Sim (from the household in 1.) in your town, you can either go into Edit Town again and evict their household, or if you have NRaas MasterController, click on them and use Total Annihilation to delete them. Hope this helped!

No, not the CAS bins but NRaas StoryProgression (SP Population module required) can be leveraged to govern the genetic sources of Service Sims. Stray animals are Service Sims. The ones that populate the adoption and equestrian breeding pools should also be governed that way, but different players report different results there.

SP is a huge and far reaching mod though, and there is no way to separate its genetics functions from the rest of it, so this requires some thought if you are not familiar with or already using SP.