*GENIUS, orange&white . GENIUS.*Things to consider:
The house around the corner where the cats are congregating is likely the house where they are being regularly fed. Cats will choose a territory where there is food security.
The people feeding the cats may have taken them to their vet to have them spayed/neutered. Or maybe not. We don’t know right now. A private vet would not snip their ears.
If the cats have been spayed/neutered/vaccinated, are being fed regularly, and there is a covered patio to shelter them from rain, then they are “home” and in the same situation as they would be in a barn cat program (food/water/shelter).
I fear you are doing a lot of worrying and planning, perhaps over 3 cats who have everything they need.
The first thing to do when you see ferals/strays which are not on your property is to go knock on the door or leave a flyer and ask if the people there “own” the cats or if the cats are unowned strays/ferals. Then go from there.
My feral Misfit spends her days outside because that’s what she prefers. If someone came to talk to me about trapping her and relocating her to a barn cat program, I’d sure be happy to let them know that she is TNR’d, well-fed, sheltered…and that she’s my cat.
It may be the cats are ferals and the people feeding would love to hear about the TNR program. We don't know. It seems like you’ve spent a week stressing out over planning Steps 2-10.
Do Step 1 first and find out the cats’ status.