Coming back to it every now and then for kicks slowly showed me a few strengths. First, with the short verb names and clear semantics, J is the only thing I've found that brings, for me, the comfort of a specialised handheld calculator to the PC. That realization, very independently from its array capabilities, is what got me really going with it, on a gentle learning curve. And you get it on your smartphone too ; I eventually sold my good old HP48 friend.
From there I started using it for small things. When I was building a lift for my brother's Warré beehives, J let me scribble a few beam-resistance equations in it and using its solver and plotter to easily get good results. So I started using it for things that were too big for spreadsheets, but that I was too lazy to deal with in a "proper" language.
That needs a change of mind regarding how you write and maintain programs. When I want J to do something in a program, I fiddle with it until I get the "sentence" right, and that's it. That sentence will never be modified again. If I need it to work differenty, I'll rewrite that sentence from scratch. Then find a good name for your sentence so that you can combine it with others, and suddently you discover that you can write J like a nice DSL that can very satisfyingly sound like plain spoken language.
I wouldn't stretch it though. I'm not passionate enough about it to invest what's needed for mastery. 80 lines of thin J is my largest. Beyond that, switch to something that helps with maintainability, but beware of the sudden and amazing code-size inflation !