I FINALLY figured out how to get free ringtones onto my iPhone. I'm putting it here in case someone else is having trouble and runs a search.
It doesn't seem to matter where the tones come from, as long as they have an m4r extension. I downloaded the tones and saved them to file, which put them into a temporary file. I then dragged and dropped the tones into their own folder in my Music folder on my laptop. Then I dragged and dropped each tone into the Tone folder of iTunes, while my phone was not connected to my computer. Then I connected my phone and waited for iTunes to do its sync routine. Then I dragged and dropped the tones from the iTunes Tone folder to my iPhone folder (but not to the iPhone Tone folder - that didn't work), where the tones automatically found the Tone folder. Then I synched again and...voila! The tones were installed on my phone.
I don't know why installing ringtones should be such an arduous process. Just about everything else about the iPhone is pretty intuitive. Maybe they make it hard because they want us to BUY ringtones?