I especially like your notion that ideas (which, I agree, are completely involuntary) are like wild-animal encounters. Great analogy!
However, I think the analogy breaks down when you say, “Like animals, ideas require care and upkeep.” I disagree with this. It seems that once you get these ideas, you feel obligated to develop every one of them. This is the part that’s causing you anguish.
You envision these ideas as being trapped, withering from neglect. They’re not, of course. On a rational level, I know that you know that this is just a metaphor and that the ideas can’t possibly suffer or experience anything.
I think it’s a good idea for a writer to keep a file of ideas. There may come a day when your imagination isn’t as fertile as it is now and you’re looking for a good one. Or, one of these ideas may work as an extension or facet of some idea you get tomorrow. They’re also great snapshots of your thinking at various times in your past. They may well allow you to access parts of your imagination that may close off in the future.
The trick is to not let them bother you. Instead, look upon writing them down as permission to forget them — for now.