I copied IndyChus’ idea and put a section of ink pen tube around the LED and that bumped the range up even more. It was a perfect fit, btw; awesome idea! I’m now getting a fairly reliable 15’ to 16’ with it. That’s as far away as I get from my fixture without taking it into another room. That’s good enough for me.
What I ended up with is a 120 ohm resistor between pin 3 and the base of a 2N2222 transistor. Well actually a 100 ohm and two 10 ohm resistors in series because I didn’t find a 120 ohm. I didn’t put a resistor between the LED and Vcc. I didn’t really see the point since I can’t saturate the transistor enough to pull enough current through it to cause an overload. I'll post an updated schematic in a little while.
I also went ahead and soldered everything onto a project board and installed it in an enclosure. Here she is.