Is 'is' ambiguous?

One of the essential components of modern logic is the view, standardly attributed to Frege and Russell, that 'is' is ambiguous: 'is' has the senses of
(i) identity (Mark Twain is Samuel Clemens; in other words, Mark Twain = Samuel Clemens),
(ii) predication (Mark Twain is an author), and
(iii) existence (Mark Twain is; in other words, Mark Twain exists), and
(iv) class inclusion (Authors are artists).

After grading a batch of logic problem sets, I'm wondering whether (i) and (ii) really are ambiguous; more specifically, how the senses of identity and predication fare with respect to the standard ambiguity tests. As I've mentioned several times before on this blog, one of the most widely-accepted ambiguity tests is the conjunction-reduction (or 'no crossed readings') test. The basic idea can be illustrated by an example: 'Alice has a bat' can mean she has a flying pet or a new baseball bat; 'Bob has a bat' has the same two possible readings, with Bob instead of Alice. However, 'Alice and Bob have bats' cannot mean that one has a baseball bat, and the other has a pet flying mammal.

Now let's think about 'is'.
'Mark Twain is Samuel Clemens' has a true reading, and
'Mark Twain is a famous author' has a true reading.
But what about 'Mark Twain is Samuel Clemens and a famous author'?
This sounds zeugmatic to me, confirming the Frege-Russell view of 'is' as ambiguous. However, many of my logic students wrote something analogous to this on their most recent problem set, when asked to translate a particular sentence of first-order logic into English. Student responses to logic problem sets are probably some of the worst data imaginable for this kind of question, but it did make me wonder whether my observations about 'is' in English are very theory-laden, ruined by years of logic and logically-inspired philosophy. What do other folks think about 'Mark Twain is Samuel Clemens and a famous author'?