Actually, my favourite example of how "strict constructionists" ignore framers' intent is the Second Amendment.
The main concern brought up that led to its enactment was that standing armies are bad and have a tendency to overthrow governments. (Jefferson especially was concerned about this.) So the whole idea of the Second Amendment was to allow soldiers in the military to disperse to their states whenever they weren't needed to serve the country, and, to keep in training for the next muster, form "well-regulated militia[s]" and keep their guns.
The second purpose was brought up by Patrick Henry and George Mason (yes, the one they named the university after), who were afraid that certain guarantees in the Constitution would lead to escaped slaves being declared free by the courts. They asked Jefferson if the amendment would allow them to form armed militias to hunt down escaped slaves and recapture them before they could get to a free state. (Pennsylvania, perhaps, or Delaware--Henry and Mason lived in Virginia.) Jefferson agreed, and so that was the second purpose of the amendment: hunting down escaped slaves before they could reach freedom.
So the Second Amendment has two purposes: precluding the need for a standing army (which, for better or worse, is defunct today since the US has a huge standing military), and hunting down escaped slaves (which, very much for the better, is defunct today). But nope, MAH GUNZ!