So I did some more work on Every Numbered Highway. Short answer is, no way it's doable in 24, and it would be challenging to do it in 48. I think I will put this one back on the shelf. As Jim pointed out, it's not quite as cool as some of the other things out there to do. I mean sure, it goes on the mantel, but maybe not in the center of the mantel.
I then turned my sights to historical markers. I'm sure you've seen them on the side of the road - commemorating various cool things. Turns out there is a website which lists them all out.
There are 67 in Hamilton County, but a lot of them are concentrated downtown and in a few other places. So that might be an option.
I also revisited EFL, being Every library in Hamilton County. There are 41 libraries, including the main library. The shortest distance is 121.53 miles, but that does not account for the fact that due to the hours of operation of the various libraries, doing it that way would force you to do it in only 9 hours. On a bike, that is even more unreasonable than the whole thought of doing this in general.
There is another route, which starts at Anderson and ends in Harrison, which gives you 10 hours (from 10 a.m. to 8 p.m.) to get from Anderson to the 2nd to last library (Miami Twp) and then another hour to do the last 8.5 miles to Harrison, which closes at 9. It would have to be done on a Monday or Tuesday. Here's a potential route, complete with actual road directions
I'm looking to do that maybe this year, maybe next year. The next big bike trip besides my triathlon is T de M 2007.