After careful consideration (see in particular #5), I think that the best syntax satisfying the difficult constraints we face (strong BC, consistency) is the following:

a ?& . b    // instead of   a ?. b
a ?& [ i ]  // instead of   a ?. [ i ]
a ?& ( x )  // instead of   a ?. ( x )

Pros

• Complete consistency between the three syntactical forms.
• Having a ?& token distinct from . is pedagogically better: One can picture the ?& token checking whether the LHS is null/undefined and performing short-circuiting if applicable, then the subsequent ., [ or ( token performing regular property access or function invocation.
• Zero conflict/ambiguity in syntax with other features, zero parsing issue.

Cons

• Somewhat more awkward to type.
• Different from other languages. (However, it is reminiscent of both ?. in C#, Swift, CoffeeScript and Groovy, and &. in Ruby.)

About the choice of ?&

• The ? recalls that we are dealing with null/undefined, as this character is used in several languages for denoting an optional/nullable value or object.
• The & recalls that the short-circuiting condition resemble the one of the && operator (replacing “falsy” with “nullish”).
• The order between those two chars is carefully designed: ?: “check for null”; &: “perform eventual short-circuiting”.