[janvanmaar]

Well, Google Reader (the experience from whose usage lymeswold wanted to duplicate) displays everything at once and does not require any manual cleaning, so I anticipated the question is how to get the same behaviour on Kindle... but I agree that it is not really clear what exactly lymeswold is asking for.
I think my reply was actually bit selfish: I would not mind achieving the 'Google Reader experience' on my Kindle either... however, I find sending incrementals to it even worse than sending entire actualizations, from the reasons I mentioned above.

EDIT: I have noticed the edition to your post now:
It depends how you name the incrementals. If they get the same name then they are moved to the periodicals collection and deleted automatically - however, they are not deleted in the right order, so in my tests in was actually the latest one that was flagged for deletion as first. And the one showed in home is actually the oldest from that day.
If the names are different then they all stay in home in the right order, you can in principle read them all and then delete them all manually...
Neither case seems tempting to me. It would require proper Kindle support.