For anyone wanting to do this trip without their own mode of transportation. This is how I did it.
On the first day I made my way from Band-e amir to Chagcharan. From the entrance gate to the national park I hitched a ride to Yakawlang. Lot of traffic so someone stopped after twenty min. From there I tried to hitchike to Lal for two hours but no luck. So I hired a provate car to take me to Panjab first as the direct road to Lal is too bad I was told. From Panjab I hired another car directly to Lal. I payed 4000 afghani for each ride. I am sure the price can be negotiated down if you try hard enough. From Lal to Chagcharan I shared a taxi with two afgans, 1000 afghani each. The first stretches are very remote and the road quality is really bad so they were very slow going. In total it took me 13 hours from the national park gate to Chagcharan. Very cool experience with great views and very friendly locals.
The second day I used public transport to travel from Chagcharan to Herat and visit the minaret of Jam aling the way. Here's how. In Chagcharan I found a mini bus that goes to Herat. The ride takes anywhere between 20-24 hours and cost me 1100 Afghani. There should be plenty of buses going that way every day. When buying the ticket I asked the driver if it was possible to stop for half an hour at the minaret for me to visit and take some photos. He charged an extra 1000 Afghani for this, which was fine by me, but feel free to negotiate. At first I felt a little bad for the other passengers as this would increase the length of their journey too. After about 6 hours the driver took the exit of the main road to the minaret and the minaret loomed into view. In order to get to the base of the minaret you have to walk or drive through the river, which thankfully wasn't very high when I got there. The entire bus seemed excited and happily joined me and took many photos, so I guess it was a welcome break. The local Taliban guys took a picture of my passport and permit and the ticket costs 1000 afghani. I did not register in Chagcharan before and my permit did not even mention Gyor as going this route was a last minute decision, but they didn't seem to care. The minaret itself is definitely an impressive sight! The rest of the 18 hours were very uncomfortable given the bumpy roads, but a very cool experience with stunning views. If you wish I am sure it is possible to stay overnight in one of the villages and break up the journey. If you are up for an adventure I can certainly recommend it!