Quick commentary on my solution. My first tries ended up quite a bit higher, but these two tricks helped me alot.
1. It is pretty well established (councilroom) that in a standard game chapel after turn 2 is much less effective. However, these puzzles are not standard games and not being able to trash the estates really changes how the card works. In this case you need to establish a bit of an economy before you thin your deck, otherwise it takes much longer to get your buying power up to provinces with all those green cards in the way. (I will admit that I made sure that I got a gold on turn 3 or 4 and if not I would just restart. I really didn't want to have too many silvers)
2. It is important to buy one hamlet early, while you are still thinning your deck, so that you can take advantage of the plus buys to get enough crossroads and additional hamlets in your deck on your none province buying turns later on.