Implications of Rice's theorem
What you forget is that all the mappings you use have to be
computable. When you state that matching cardinalities ensure the
existence of a mapping, that may be true, but the mapping is unlikely
to be computable, precisely because that would let you get a
contradiction with Rice theorem. In computability (at least for what I
know of it), everything is either finite or countably infinite. So existence of
mappings is usually not an issue. The problem is whether it is a
computable one.

To say it differently, there is certainly a mapping (actually
uncountably many) that associates precisely palindromic words with
total computable functions. But, given such a palindrom $w$, which the
mapping associates with a function $f_w$ there is no way you can
actually use such a mapping to get the result of applying $f_w$ to
some argument. You mapping does not give you any way of identifying
the function or computing with it. Your language has non computable
semantics.