The signal is significantly better than before (reaching over 100 MPS downloads when it is working), but it is still not quite clear enough of obstructions to keep a signal consistently. At least it has been receiving enough of a signal to give us a "map" of the obstructions. Based on this, our second location (which requires either using my ladder at its highest extension or outright climbing on the roof and leaning slightly over the edge of it) should work. However, there is no way that I am attempting that unless it is in daylight--which means that I should do it this Sunday afternoon.
I am not looking forward to taking it down from its current location, but I'm particularly concerned about putting it up in the more difficult location. In fact, I'm almost tempted to skip that spot and move directly to the third spot I had chosen (the top of the central gable of the house) despite it absolutely requiring that I lean over the edge of the roof to attach it there. Hopefully, we will find that the second location is easier to get to than I currently fear and that it will be absolutely clear of "obstructions."
A note for those who are thinking of getting a StarLink: the dish spends its booting stages pointing straight up, but its default orientation is due north. That orientation needs to be completely clear--the higher you can place the dish, the better. Part of my problem is that my house faces northwest and there are a line of trees (probably too close to the house) directly to the north so that I cannot use the northernmost location on my house.