perhaps first copying whatever output you care about, so that it doesn't get destroyed
Well, yeah. You're going to use up negentropy for that - where are you copying to? Reversible computing just means you spend less negentropy. (Feel like I've said this before.)
Yes, you just produce less entropy. But you produce a lot less entropy and it is completely unrelated to Landauer's principle.
Suppose I want to calculate a 1TB document created by a googol person civilization running for a googol googol years. I only have to produce a TB of entropy, not more than a googol googol googol bits (as I would have to if I used irreversible computing naively).
This post may be interesting to some LWers.
In summary: it looks like our universe can support reversible computers which don't create entropy. Reversible computers can simulate irreversible computers, with pretty mild time and space blowup. So if moral value comes from computation, negentropy probably won't be such an important resource for distant future folks, and if the universe lasts a long time we may be able to simulate astronomically long-lived civilizations (easily 10^(10^25) clock cycles, using current estimates and neglecting other obstructions).
Has this been discussed before, and/or is there some reason that it doesn't work or isn't relevant? I suspect that this consideration won't matter in the long run, but it is at least interesting and seems to significantly deflate (long-run) concerns about entropy.