Cut-elimination for calculus with nats or other inductive datatype?

Does anyone direct me to a paper detailing a cut-elimination theorem for propositional intuitionistic logic, including an inductive datatype such as the natural numbers (lists or trees would be fine, too)? An example of the kind of system I am interested in is Godel's T, which has types given by the grammar $A ::= \mathbb{N} \;\;|\;\; A \to A'$. I am not very interested in quantifiers over natural numbers or predicates indexed by natural numbers.

I know how to prove beta-normalization for natural deduction version of these systems using a logical relations argument (or related techniques such as NbE), but would like to know if there are standard references on how to adapt these methods to sequent calculi.

The reason I ask is that I am studying adding fixed point operators for guarded recursion to a language. The denotational idea is a rather old one -- interpret types as ultrametric spaces and fixed points via Banach's theorem -- but the purely syntactic techniques I know for proving cut-elimination don't seem to adapt that well.