We attempted this route about two years ago and, due to my extreme lack of experience at the time, failed miserably. Luckily, Rachel can't back down from a challenge so I got her to try again. This time we were determined not to fail.
The Alder Saddle Trail (or what's left of it) is nothing like we remembered. There were sections to bushwack through to get to the top of the saddle but I've definitely done worse. We also kept re-finding the trail pretty easily-- no route finding issues like last time.
From the saddle to the summit is a whole different story. We took the advice from Preston's description and stayed a bit low on the south side of the saddle to avoid the thicker brush. The terrain begged for us to stay south instead of heading back up high and attacking the ridge directly from the east side and that turned out to be a bit of a mistake. From a distance, it appeared that we'd be able to make our final ascent from a bit southeast of the summit. As we got close, we found out that it was not going to be possible. We backtracked a bit northeast until I could find a spot we could summit from. Fortunately after some bushwacking, I found a spot we could climb up. It was a bit sketchy but I felt like it was pretty do-able. Rachel's opinion was something similar to "this is really stupid and dangerous but what choice do we have?"
Soooo.... we made the summit and it was worth all the effort. We met a few other hikers at the top and ate some lunch. We eventually made our way down the chute and headed back to the trailhead. It's been quite a while since I'd been up Browns and had forgotten how treacherous that chute actually is. It gave us a little added adventure on the way down.
After finally accomplishing this, I'm kind of surprised that more HAZ folks haven't done it.