Thank you everyone for your replies. I have no idea how much it costs to get large plants removed, but I may have to look into it. Someone elsewhere suggested maybe limbing them up and planting stuff underneath. Not sure how that would look, and it wouldn't fix the height problem. Can I just cut off the top foot or two?
If I ever do get them removed, I would like to install a native large bush or short tree in the corner and a smaller bush closer to the porch. I suspect that mountain laurel would do well there, given that the azaleas in front thrive. Plus it has the benefits of being evergreen and becoming gnarly over time. Any thoughts on that idea?