While I agree that parsing might be problematic (high priority concern), I confess at the same time that I found myself actually wanting to be able to define this kind of DSL-syntax more than once in the past.
I want that kind of DSL too, but I think the cleaner way to get it is probably to introduce ephemeral types. An ephemeral type cannot be stored or discarded; the only thing you are allowed to do with it is immediately call a method on it. Then you could build things up a piece at a time using more or less normal parsing rules.
(In a sense, every mutable operation could be viewed as changing an ephemeral type, but here we make explicit the type and the operation converting it to another type.)
This reminds me a bit of similar Smalltalk syntax which I loved. Why limit it to extension methods? I would prefer that we were able to write all methods in this syntax as it leads to far more comprehension of coder readers, at least for the left-to-right natural languages. Right-to-left languages could simply reverse the argument order, if desired.
In effect I do this now, as I have case classes and opaque types, and everything else is put in with extension methods.