Thanks, everyone!

Before I turned in last night I tried putting the amplifier on the antenna end and it definitely made a big difference. I got all the channels I wanted, though a couple are a little wonky. They work for recordings, though, where the pauses get evened out.

So just now I removed the amp entirely and while I seem to get fewer of those fringe signals I also seem to be getting a more reliable signal from the channels I wanted.

But your suggestion to put the HDHomeRun on the antenna end is a fantastic one. That thought crossed my mind briefly but I don't know why I ignored it. I think it might be out of concern for the affect of temperature swings on the HDHomeRun. The antenna is on the inside of my garage, facing the outside wall like it's the class dunce. I'll probably make a little shelf for it since the mounting hardware is on the wrong side now, and affix the HDHomeRun somewhere around that. Good idea on that part. I shouldn't have much drop in signal then!