What fraud are you trying to prevent that gets abused in a free service? Most of the abuse I see for free services I host is DDoS, brute-forcing paths/authentication and port scanning, but all of those are trivial to deal with rate-limiting.
My wife ran a small business for awhile that catered to local customers only (i.e. not an online business, products didn't ship through the mail. She added a contact us type form which submitted to google forms as a quick alternate to phone calls for prospective clients. It was used almost exclusively by people trying to sell her things from overseas.
She wasn't even running ads or anything online, so how they ever found the website in the first place, I have no idea.
Please don't do stuff like this. Some of use use VPNs and aggressively block third party JS. These sorts of shenanigans render many sites unusable which is frustrating but simply not using those services is a price I'm more than willing to pay at this point.
Are you describing nonces? A nonce is basically a "secret" (due to SSL encryption) number inserted into the HTML and submitted via a form. You don't need JS, just SSL.
Making it require JS is on purpose as a lot of spam robots only parse HTML and don't execute JS, so you get less spam that way.