Jonathan Robie, the forum owner, kindly gave me permission to post this.
In your post, you asked for "parsing practice". It so happens I have written a software program which gives you precisely that. It's called "Paradigms Master Pro", and you can download a free evaluation copy here:http://paradigmsmasterpro.com/
The idea behind the program is very simple: It gives you a question, namely a word-form in Greek (or Hebrew), and you must answer by telling the program what it is, morphologically speaking. Then the program tells you whether you were right or wrong, and gives you the complete list of correct answers. If you were wrong, it attempts to give you the form that would have been the question, had your answer been correct.
The premise of the program is twofold:
1) Repetition is the mother of all learning, so we should provide that, if recognition and identification of forms is the goal
2) Variation is important in repetition -- otherwise, repetition gets boring and counter-productive to learning
The program give you both: Repetition and variation. And it knows more than 2800 forms for Greek, all carefully hand-curated in their analysis. It provides quizzes on verbs, nouns, adjectives, the article, and even certain aspects of prepositions. It also "gamifies" the process of learning, keeping a score which you can use to compete against yourself.
The program runs natively on Windows(R) and Mac OS X(R). If you wish to use it on Linux, the Windows version works for me under the "Wine" program on Linux.
There is a short video on the website which you can watch to get an idea of the program. And the evaluation copy is free to download.