I mean, maybe we could be a group of 40 or less and get together and run a low-cost version of the Bitcoin network with a few nodes and a limited number of hash miners between us, like in the early days.
You mean a clone with no value whatsoever.
There is already a network for you, it's called testnet, and seems like it has only 500Th/s right now, so you could mine not just one but quite a few coins even with an old ASIC that is valued at scrap metal price.
re: Testnet. Keep in mind that any coins mined on it are eventually supposed to be either donated/returned back to the Testnet coin faucets where they are originally generated. For example the
one ran by mempool.co Testnet and its coins exist for the sole purpose of testing mining software - not for mining and accumulating Testnet coins. It is expected that after testing is done all coins generated are returned to their source. Folks mining Testnet coins and then hanging onto/selling them is why it's up to v4 or such. To stop that each version makes the older ones unusable on Testnet.
As for making a clone coin it also must be said that you would be creating yet another worthless altcoin - it cannot/would
NOT be "Bitcoin".
BTC is 1 specific crypto coin and in-turn 1 specific protocol and blockchain, period. "Bitcoin" not a generic term for any other crypto coin including those that do use sha256...
That said, coming up with your own coin just for the heck of it can be fun. Something like
five thousand or more altcoins have been created just for that sole purpose. Heck, a couple including of course Dogecoin are even worth something.
Given that fact this thread belongs in the altcoin areas of the Forum or at best
the General Bitcoin Discussion area - not here in the BTC-only areas- so expect the mods to move it.