I've been using git at work for a couple of years and I haven't spent very much time thinking about the internals at all. It just seems to work pretty much, though sometimes I get into a weird state and just delete and redownload.
You say I have very little excuse for my ignorance, but I would also say that I have very little excuse to spend any more time learning a tool with as many dark corners as git.
If you're about to do something 'weird' like fix a merge conflict, you can save the changes by creating a branch.
Sometimes you have to go back and fix a previous commit to reconcile a conflict. The 'gitk --all' command is your friend here. With it it's easy to visualize the history, reset, cherry-pick commits, etc.