Other than the official threads, I have never tried the adopt strays LTW (using true strays) because, in my experience, strays never stay long enough to get the friendship significantly raised and their return is very unpredictable. They turn up every few days, but, frequently the timing is inconvienient (not much use if your sim is in bed or in the shower etc.) and most frequently, when they arrive, they just go to sleep immediately. Waking them up does not seem to work, they simply get up and leave so interactions are greyed out. The one time I got close to an adoption, we were at good friend's level, the stray died on my lot and I ended up with a permanent red ghost cat on my lot.
You can increase the number of strays on your property by buying the gnome which you can set to encourage/discourage animal visits. Make sure your sim has the correct animal lover trait and that you have the "Raised by Wolves" reward.
