CAUTION: don't mess around with mains, unless you know what you're doing. Please excuse the less than stellar production quality of the video, wanted to  make a quick video at the bottom showing that it does work as per the contest rules.  I had some stuff laying around, including a small solid state relay (SSR),  so I decided to make a remote controlled light for the fun of it.  The little SSR only gets slightly warm with a 40 watt incandescent bulb (the SSR is rated for a max of 1 amp.)

In other related news, I've ordered a proper MOSFET that should work well at a low voltage, allowing me to crank the power to 11, to see if that problematic TV will play nice with an IR LED putting out around 800mA of peak current. I did try using more cells to boost peak current output a bit (to around 400mA or so) a few weeks ago, but even that was still not enough to get that problematic TV to behave.

It also does not seem to make a great deal of difference (in my limited testing) of either using a crystal vs. using the internal oscillator. Still, it doesn't cost much to get a considerable boost in stability an accuracy.