You asked "how do you know your vote was counted". You can google for examples of how this works in verifiable voting systems.
Just pick a voting station with lower computer literacy, and you can do whatever you want ..
Different solutions exist for this problem, which is known as a "clash attack". For example, in the Floating Receipts voting scheme, those things that you call "recipes" are pre-printed on ballots and hidden under scratch strips. The scratch strip is removed at the time when the ballot is dropped into the ballot box. If the manufacturer of the ballots were to pre-print the same "recipe" on multiple ballots, it would be discovered during the verification phase, because you would in some cases have 2 different votes cast on 2 different ballots which would contain the same "recipe". So both voters look up the "recipe" online and they are supposed to discover only one vote corresponding to the "recipe".
Cryptography. Your receipt is presumably only valid for yourself. So if you got someone else's receipt, it wouldn't be valid for you.
I support paper voting for political elections for most of the reasons you mentioned, but I don't think that automatically makes all arguments for paper voting good and valid, and all arguments for alternative voting systems null and void.
And even if political elections are better done on paper, there's plenty of other elections (eg in companies and clubs etc) with different requirements and threats, and they might benefit from the research and experimentation.