Cambridge Dictionary's advice is to stick to past simple and past perfect constructions when using would rather, although it's not exactly phrased as a commandment: "when the subjects of the two clauses are different, we often use the past simple to talk about the present or future, and the past perfect to talk about the past". http://dictionary.cambridge.org/us/grammar/british-grammar/verb-patterns/would-rather-would-sooner
So Cambridge would suggest you stick with either:
- I would rather you did it., or
- I would rather you had done it.
That said, the following are not offensive to my ear:
- I would rather you do it.
- I would rather you were the one to do it.
- I would rather you were the one to have done it.
However, all I've really done here is circumvented your question by creating a root past simple sentence (I wish you were the one) as suggested by Cambridge and then making it very close to sounding like the sentences you are trying to make but actually not the exact form.
My best solution for "wish" would be very similar to the above. As noted on Perfect English Grammar, the use of "were" with "wish" is generally in the "Wish + (that) + past simple" form and the site gives the example "I wish I were rich". http://www.perfect-english-grammar.com/wish.html
You can modify this form as I did above to create:
- I wish you were the one to do it.
- I wish you were the one to have done it.
Again, this sounds very close to the words you suggest but ultimately I am skirting the whole problem by making it a past simple sentence.
Sorry, I can't think of any way to get closer to the sentence structure you are suggesting that doesn't sound overly offensive to my ear.