I have done some work in this area, mainly to try to understand the
subject. In this block I include two published papers, one set of
notes (which ramble a bit), and two unpublished papers (which in their
present state are not ready for publication). I also include the
slides of a talk that I gave at the Leeds meeting in July 09.

A pre-publication version of the paper

A comparison of two systems of ordinal notations

Archive for Math. Logic 34 (2004) 65-83.

Comparison.pdf
.

A pre-publication version of the paper

Fruitful and helpful functions

Archive for Math. Logic 47 (2008) 677-709.

Fruitful.pdf
.

A long set of notes

Iteration templates as generalized ordinal notations

IterTemplate.pdf
.

First unpublished paper

An applied lambda-calculus for iteration templates

LambdaH.pdf
.

Second unpublished paper

Generating ordinal notations from below with a non-recursive
construction of the Schutte brackets

FromBelow.pdf
.

And the Leeds slides

OrdSlides.pdf
.