Just a couple of additional comments to complement what Mike and Simon have said.
The complete walk is long. But, I am nearing the end of my seventh decade, and last year I started from the entrance to the Sfakiano gorge, walked up to Kalli Laki, on to Anopolis, and then down to Loutro. It was, indeed, a long day - about 12 hours. But not overwhelming. I had plenty of time to rest, and enjoy the views.
I agree with you that the road from Imbros is long and boring. I strongly urge you to take the path up from the Anopolis side. It is not in very good shape, and can be hard to follow in parts. But, it's worth it. You go up to as high as 1300-1400 meters. It's very peaceful, and you have some great views.
If someone gives you a drive part way up, the path starts at the switchback that can be seen on Google Earth at about: 35Deg 15' 57.04" N; 24Deg 07' 11.95" E. The path is just to the right (east) of a ravine that crosses the road there.
I don't have the type of details about the path that Mike might be able to provide. Some places are obscure. There are red dots to help you. In places there is good kalderimi. Basically you go mostly north for a while, before turning east, and then at the abandoned fields surrounded by a stone wall (35Deg 16' 15.54" N; 24Deg 07' 43.72" E; the open spot you can see on Google Earth) you turn mostly south, down a ravine, into Kalli Laki. As best I can tell, there is no path down the ravine, and there are no dots after you leave behind the stone wall. If you go down the ravine you'll end up in Kalli Laki.
Once in Kalli Laki I recommend that you take some time to explore the ruins of the stone houses. They have some features I've not seen elsewhere in Sfakia. One has a very well preserved stone arch.
Mike has provided excellent instructions for finding the path down to Aghios Paulos. However, he is more sanguine than I am about the state of the kalderimi. It is true, that, for the most part, it is in pretty good shape. But, there are places where you have to look carefully and where you could go wrong - especially on the first bit after you leave the crest of the hill. The blue dots will help.
Enjoy the walk.