Going to answer my own post here, after just completing this climb. It was totally awesome, and worth the trip, but I do not recommend it for an inexperienced climber.
It is relatively easy to get there via public transportation. There was a bit of an issue with the OBB (Austrian train service) from Vienna however, as part of the route to Hallstatt (one of the the nearest towns with a train station) was under construction and they were running buses instead. There were a couple very tight connections (under 10 minutes) and the buses did not wait for late trains, even though they were supposed to be a service for train customers affected by the construction. This led to a 50 minute wait for another bus for about 40 people one day.
There were local buses from Hallstatt center (Hallstatt Lahn) to a very tiny stop about 10 minutes north (this is on the west side of the lake) called Gosaumuhle, where you have to switch to another bus that takes you all the way to Lake Gosau (Gosausee). Unfortunately, the bus system does not time this common transfer very well, so you have to wait 40-50 minutes between buses. Kind of a hassle, but you're going to a pretty amazing out of the way place, so...
The Gosausee bus route ends right at the cable car (Gosaukammbahn) that runs about every 15 minutes. Its about 22USD for a round trip ticket, otherwise, add another 1.5 hours of hiking each way to get to the trail head. As it is at least a 3.5 hour climb up and 1.5 hour hike back down, most people seemed to opt for the cable car.
Also right at the cable car platform is Sport Jirka, where you can rent the harness and lanyard you must have for this climb. They were great in helping me reserve my gear in advance (about 29USD for the day) but they had tons of kit, so reserving probably not necessary. I didn't notice until I was outside that the carabiners on the kit they gave me were a bit worn, because I was distracted by the gal at Jirka telling me that weather did not look promising for that day, and asking if I wished to not go. Weather is a real issue for this climb in summer, as this part of Austria gets LOTS of rain then. She showed me weather radar and a forecast, and said it looked like there would be a window of good weather around noon, so I decided to go for it.
My biggest concern was how busy this route would be, especially on a Saturday . Because of the buses, I was not able to get to the cable car until around 9:30. It didn't seem too busy at first. It was overcast and the prediction of rain before noon probably scared a lot of folks off.
The rain came about an hour in, and made it quite slick; the foot pegs and handholds slippery from both water and mud. If you are not a very experienced climber, you should not do this route if there is a chance of even light rain.
There were quite a lot of people doing the route that day despite the rain. And a number of them put others' safety at risk because they could not handle the route and had to go come back, forcing them to pass us, often at very narrow points. There were even a couple of ---- who did the route backwards and ended up having to pass people right at the most dangerous point on the climb (right above the ladder). Don't be those guys!
But the sun came out right in time for the amazing "stairway to heaven" and the summit, and it was beautiful! There was a bit of a line (maybe 25 people?), as some folks who were not really prepared for the intensity of the ladder climb asked to not have others on it while they climbed (which people respected), and this created wait. So again I would say if you're not somewhat experienced, don't inconvenience others or worse, put them at risk, by attempting this climb.
As some forums have noted, the hike back down is pretty rough. There are even some areas on it that have safety cables. In some ways it was tougher than the climb up. Hope this helps someone.
Happy climbing!
