Excuse the verbose reply, I had a bit of a challenge finding a single phrase and I came to the conclusion that it's kinda hard to describe the activity of trialling various approaches, investigating leads, and analysing the problem, and the stage of analysis you're at in one go - in my head, these aren't strongly coupled.
If I extrapolate out and imagine that you can skip past it all and just want to express the current result of your work, that's a third thing, but I figure that might deliver the most relevant information in one go.
So, with that preamble:
If you're after something to express that you're getting close to really understanding the project/issue, you could say that you were getting a handle on it. That would be providing a sense that it was a problem that you didn't know how to solve before, but that you're getting to a point where you know how deal with it, or that you're getting a clearer understanding of it. (Another alternative for this sense would be: getting your head around the problem.)
As a sub note if you're wanting to emphasize the sense of getting past the distractions and getting close to the real issue, you could also say that you're getting to the heart of the matter.
If you want to talk about what you've done to get to that point, I can't think of anything I'd use in preference to exploring the issues (which you've already got), or perhaps exploring alternatives. If you're trying to express that you've done all the required things as specified in a procedure or something like that, perhaps something like done due diligence? (someone might want to sanity-check me on this one though, this could be a very localised public service usage)
If you want to say you're still working on the problem - then you could be still hashing out the details (actually working and defining out detail), working your way through to the nitty-gritty (getting to the detail), or be in the thick of it (some unspecified point, probably nearer to the start, rather than the end, where it's still a bit unclear)
If you wanted to put all of them together for the fun of it...
Boss, this week I've been exploring alternatives and I think the team is slowly getting a handle on the issues. We're still in the middle of hashing out the details but come Monday? I think we'll have got to the heart of the matter and will be ready to present you a solution.