Here is a document proving that even the Pontifical Commission for the Editio Vaticana was aware that most parishes could, perhaps, not easily sing the melodies between the Epistle and Gospel. Since that time, many have made “simple arrangements” of these chants (the Gradual and Alleluia Verse).

Solesmes published two version of the Chants Abrégés, which can be located at GoupilChant.org, along with recordings. Richard Rice has published simplified versions. Justine Ward also published a very beautiful collection (6.5MB PDF). Caecilia published several interesting versions, as did many others, as well (e.g. the 1917 Schwann Graduale).

Probably the easiest (for amateur singers) are the Graduals and Alleluias published in the Mode II Psalm tone versions at GoupilChant.org, which have been carefully typeset:

I recently discovered that Max Springer also composed simplified versions (in his 1910 organ accompaniments to the Graduale), and here’s an example of one.

All the books mentioned in this article (and hundreds more!) are available for free and instant download at the Lalande Library of Rare Books, a ministry of Corpus Christi Watershed.