Find attached a patch for this.
The stemming is done by KuromojiKatakanaStemFilter, which has been added to KuromojiAnalyzer and a corresponding KuromojiKatakanaStemFilterFactory has been added to the text_ja field type in schema.xml.
Note that this stemming is now turned on by default and I think it makes good sense to do so. The minimum length of a token considered for stemming is configurable and I've made the default of 4 explicit in schema.xml to convey that it's there.
The stemmer only supports full-width katakana and should be used in combination with a CJKWidthFilter if stemming half-width characters is required and you're doing your wiring. Both text_ja and KuromojiAnalyzer takes care of this, and the default overall processing is the same.
There are some test cases in TestKuromojiKatakanaStemFilter, but I've added a case to TestKuromojiAnalyzer that demonstrates how the stemming works in combination with katakana compound splitting.
In Japanese, "manager" can be written both as マネージャー and マネージャ (and probably also マネジャー), and for the compound シニアプロジェクトマネージャー (senior project manager), we now get tokens シニア (senior) プロジェクト (project) マネージャ (manager), and we've stemmed the last token by removing the trailing ー. Kuromoji also makes the compound シニアプロジェクトマネージャ a synonym to シニア, and ー is also removed for the synonym compound.
Tests pass and I've also tested this end-to-end in a Solr trunk build.