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I'm developing an application on Bitcoin blockchain, and I use output transaction scripts that are not standard according to the classic payment methods. However, even so, on Tesnet everything works fine but I recently read on Bitcoin site the following:

So, appearently, Tesnet may relax some restrictions on transaction scripts, but it doesn't specify much more. So, now, I have no way of knowing if such output transaction scripts could be accepted on the Mainnet, except by buying some Bitcoins with money that I really don't have, and I'm also starting to wonder what is the purpose of the Testnet if its behaviour doesn't reflect the one of the real net and, even worse, what is the purpose of having a script language with such multiple instructions when you can actually use just a few of them. Is someone able to give me more informations about all this? Thanks in advance.
Thank you very much for your exhaustive answer. The fact that I can't use P2SH is because this requires the redeem script to be known by the sender (so he can include the hash in the output script) and the receiver. In my setting, instead, the redeem script is known only by the sender. – Daniel – 2018-12-04T18:29:15.477
That doesn't really make sense. How does the receiver know he's being paid if he doesn't know what output script to look for? – Andrew Chow – 2018-12-04T21:57:37.253