Good suggestions, Andrew, thanks.

I took a picture of the place the lower, long bolt goes, in case it's any help for any future reader working on getting the alternator out. I think this spot is the main pain point. There's not much room to get the part of the alternator that goes over the back and the bolt screws into over to the right to free it up. Also, the cylindrical piece, not sure what it is, behind it with the square metal protrusion on it, is closer than it appears on the picture.