Found The Solution!
Interesting. In the process of typing up suggestions for this, I figured out what the problem is, then took another 20 minutes to find the fix. I also, while looking, stumbled across two incredibly useful features that I did not know were even there, which is awesome. Seriously, AWESOME.
Here's what's going wrong: If you type わたし once and then bring up the suggested predictions list for it, but instead of selecting the correct character select わ足し instead, it remembers that as your preferred choice. You probably accidentally hit space an extra time without realizing it or something.
The PROBLEM is that once you've done that, the suggested prediction that pops up with わたし will ALWAYS assume you just want options for the first character, and will NEVER suggest all three. I'm nearly certain this is a bug, maybe quite recent (I'm using 10.6.2, and I'm sure it worked properly in 10.5.something, not to mention if it had been around for a while surely people would have complained and/or fixed it).
The prediction list that is causing the problem here is stored in ~/Library/Preferences/com.apple.JapaneseAnalysis/
That's a folder with a number of files in it, but I couldn't easily figure out which was the problem or how to edit them. If, however, you trash that whole folder, log out, and then log back in (or reboot), your preferred predictions will be forgotten and you're back in business. You'll also lose all the correct ones, but that's probably not a huge problem.
Perhaps someone else knows how to edit the dictionaries manually to remove the bad association, though really this issue should never happen in the first place, because the OS should be offering predictions for the whole word if the first-character suggestions aren't sufficient.
Also, it seems like the Kotoeri preferences aren't working; the check box for "Show predicted candidates" doesn't seem to do anything on my system, but if I understand what it's supposed to do correctly it should stop Kotoeri from suggesting any previously-used selections at all. Maybe I just don't get what it's supposed to do.
I'd be really interested if people could try this and see if it creates the same catch-22 for them. Particularly curious if it's new in 10.6.something, or if it has existed for longer. A little more data to submit a bug report to Apple would probably be useful.
Now for my two peripheral discoveries: First, I found out that the OS already has a huge Japanese-English dictionary, plus a pure-Japanese regular dictionary, built-in. You can turn them on via the preferences of Dictionary.app. Had no idea that was in there, but SO useful.
Second, I thought that Apple had dropped the preference that allowed you to switch between a per-document input method and a systemwide input method in 10.5. I preferred systemwide, so this didn't bother me, but my wife liked the other, as did some people here asking where it went a while back, and I thought there was no way to switch anymore. Turns out that it's there, it's just in a different place--it now appears to the right of the Input Sources list. I could swear that wasn't there in 10.5, so maybe they put it back in 10.6.
Either way, sweet for people who prefer the old style method.
Wasted a bunch of time digging myself out of the hole I created trying to help, but I'm happy anyway!