We checked with the RAE (The Royal Academy of the Spanish language) and they give an example where cualesquiera is used in front of a noun too. As cualesquiera is hardly used nowadays it is difficult to find sources referring to this, but if you want to share some of the sources you found confirming the only acceptable position is after the noun, please do share, so we can look into it and double check.
If as stated in Inma's response, "cualesquiera is hardly used nowadays," what should I use instead to refer to a plural noun, e.g., "He reads whatever books he can find?"
I think you'd often avoid the plural and use singular. I would prefer this in the "any methods" example. If a number explicitly is mentioned as in the other example, this obviously isn't possible.
I went through a lot of book search results for cualesquiera, and found that it seemed a) fairly often used with singular (in error?), b) more common in Latin American Spanish, c) more abundant in older literature than in recent one.
Some examples were from math books, like >>Sean dos puntos cualesquiera P y Q y sus homólogos P' y Q'
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