Re: Teaching an outdoor cat where home is--no judgements please
Here are my thoughts, I'll try to keep them organized:
She has been successfully relocated and the 4mo she's spent on your porch are enough for her to know *this* is her new, best home: love, comfort, safety, food. My ideas for getting cats accustomed to new areas, is basically I want them to be able to recognize our home from all sides, both sight and smells so if they accidentally get out, they can find their way back. I would let her out of the cage and just take her on short exploring-walks. If she will accept a leash so you can prevent her running off, that would be great. Otherwise just walk around with her, kneel down and call her attention to things, like plants or fenceposts she may like to smell. Some cats will run if you follow behind them, some are more confident following their person for a bit before they feel confident being followed themselves.
Watch her comfort-level as you go exploring with her. Talk to her and pet her to reassure her. Return her to the porch-crate when she seems to get nervous. Allow her to stay out longer and longer before returning her to the porch-crate and eventually just leave her crate-door open so she can come/go as she pleases.
*another thing I do, is I have a particular "call" I make to call the kitties to me. I use this at feeding, grooming, treat-ing and play times. Use this to call her to you for her scheduled meal times and to just generally call her to you if she is out/about but near enough to hear you call.
When she is comfortable in/out of the porch-crate, you can add something else for her to use, maybe a small and enclosed sleeping area for winter weather protection and possibly a tall-ish perch to give her a commanding view and keep any stray dogs from reaching her. After she has grown accustomed to the new sleeping/perch-thing, you can remove the whole crate system and have your porch back.