But I haven’t been able to find much documentation on how to do this sort of thing, or links to sites or services that can make this happen.
Which also leads me to believe that maybe we could start up a business helping others to do this sort of thing?
Anyway, what sites or resources am I missing?
Doge is a fork of Bitcoin, but not actually very interesting as a cryptocurrency (e.g.: https://github.com/dogecoin/dogecoin/issues/1674). It's the "fork the codebase" approach that vimy's comment mentions.
Newer currencies generally don't fork the codebase of an existing one. Shiba Inu is an Ethereum smart contract (ERC-20).
Interesting places to start reading are about smart contracts (ERC-20 on Ethereum), parachains (on Polkadot) and also just browsing around coinmarketcap.com (e.g. you can find security reviews of various contracts, which can be very interesting reading).