I'm looking for kitten help after Memorial Day weekend.

So, every year I go to E.Kentucky a couple of times. Usually its Memorial Day and August. A couple of years ago, I was there in August and found out one of my cousins has a cat colony on his property he refuses to do anything about. Financially he could, but he's too cheap. There was a 4 or 5 week old kitten abandoned by his mom who would hang around my Aunt's house. He had two littermates that were picked off by who knows what, and I assumed he would not survive if I left him. So, he came back with me and I got him adopted through SICSA. I paid for it myself. Well now, I asked my cousin what the kitten situation was so I could be prepared with traps and carriers when I went down there Memorial Day weekend. She said that 4 or 5 have had kittens in the last month or two. There are A LOT of variables. I don't know how many there are. I don't know if I'll catch all of them. But what I do know is I need to be prepared in case I get all of them. I reached out to some rescues yesterday, and explained the situation and it's too soon to say if I'll hear back, but I may be stuck paying for 25+ cat vettings because I can't find rescue backing. Any constructive advice would be helpful. Thank you!