It wasn't on FFnet (at least, not anymore) but I was able to find the Harry Potter and the Kindling of the Fire series on AO3. I started it a few days ago and dropped it, but was able to refind it on AO3 by searching the Time Travel tag and then filtering by only the Harry Potter works mentioning Charlus Potter.
It has a lot of parallels to your question which I will detail here:
Harry is known as a Peverell; I don’t know if he is the MOD but I do know he is living in Peverell Castle
Harry is in contact with Charlus?
He definitely went back in time, as he is friends with Charlus
Harry is using the town on Peverell land as a safe haven for squibs, and creatures; he has a town square and even a knight bus station in town.
In the first, titular work of the series, all of this occurs; Harry wakes up in the past and meets Charlus Potter at St. Mungo's, who then proceeds to give him the title of Lord Peverell and the Perevell Castle and associated estates. Charlus convinces Harry to start an orphanage/sanctuary in exchange for the land. In Chapter 5 of Laying a Foundation (the second work in the series), it is mentioned that there is a Knight Bus station there.
There is a Stone circle or two near the town
I’m 90% sure he is making the castle into a school, and there might be a primary school for magicals?
covered in Chapter 4 of HPKoF and Chapter 1 of Laying a Foundation
- I remember him submitting paperwork to the ministry and searching through interviews for teachers
Chapter 3 HPKoF
They get a mason/stone worker who is a squib with a “muggleborn” son; the squib might have cancer of some kind? I do know he is sick and they use magical treatments to make him better
Harry visits orphanages and takes in any magical children; he can sense them but he uses a stone to see if they hav magic of any kind
Some relevant parts of Laying a Foundation, chapter 3:
“Now Mr. Waldecott, what is the matter with you? I might be able to help.” Harry said to the boys father.
"Appendicitis with complications and complications I'm told."
Harry leans forward, and gives Mr Waldecott a small stone from his bag. When the man closes his hand around it the stone glows a soft blue.
“Well I'll be. Does this glow mean I'm one of those squibs?”
“Yes indeed Mr Waldecott."
“Well Headmaster I don't know as how I'll be much use to you, I was a stonemason by trade afore I started at the factory as a foreman.” Mr Waldecott muttered.
It is also true that Harry was running around collecting orphans/students, but it's because he was asked to by Headmaster Dippet in this passage from Ch. 2 Laying a Foundation:
“Well yes, but frankly I think Albus has too kind a heart. Our number of muggleborns attending has dropped in the last few years, and there are many that graduate Hogwarts and leave the magical world entirely. Which is a tragedy. So if you could give them a talk, and well do whats necessary ….” Headmaster Dipper[sic] waves his hand vaguely.
There is a town located near them, it’s run down so they go searching through the rubble and find plates and such with the Peverell crest
Chapter 2, Laying a Foundation:
As we've been rebuilding the outbuildings and village we've found all sorts of lost treasures. They had some very strong preservation charms then.” Harry thinks its not so much the charms, but the fact that the streams of magical power had been stronger and better tended six hundred years ago.
Harry goes to Wools and gets a young Tom Riddle
Chapter 5, Laying a Foundation. He uses the stone as mentioned earlier to test a few other orphans while he's there, and picks them up too.
Tom follows Harry one day to one of the stone circles
Harry has trunks with all the magical creatures from his time in them; in Harry’s time the world has fallen to ruin due to muggles and magic has disappeared
Not all the creatures within the trunks survive
All answered here with this passage from chapter 6 of Laying a Foundation:
[Tom Riddle] stared up at Hyppos. He is trying to control his features, but his small face is shadowed with confusion.
“You were in a tent in a box. How can you be alive?”
“When the tent is folded the enchanted space within pauses in time, and all within it.”
“The other tents ...they were all dead. I don’t even know what half of them were.”
Sorry for spotty quotes, I don't feel like combing and just grabbed the ones I particularly remembered or were easy to grab.