What I think we could do without too much trouble or overhead is to set up errcontext data so that a failure like that could come with a CONTEXT line like
ERROR: invalid input syntax for type double precision: "A" STATEMENT: insert into x (a,b,c,d,e,f) VALUES ($1,$2,$3,$4,$5,$6) CONTEXT: reading parameter $2 for statement "foo"
I'm curious whether that would be enough information to solve your problem.
I ran into this same problem a couple weeks ago, your suggestion above would have supplied enough information to debug the invalid input without having to jump through hoops at the application side.