I think that in general people look at their actions as outside of "nature" they look at things as natural or things created/influenced by humans, that's a little bit contrived because people are part of nature... anyway I think that putting things in "natural" or "not-natural" categories might be misleading and irrelevant and a lost of time for this discussion so I'd like to eliminate this from the beginning. So, I'm not willing to discuss about things being natural or not being natural (unless you define that more clearly).
As for us "interfering with the natural course of life" it depends on what exactly you mean by that, but to me it seems that's what we do as humans (by definition: see my first sentence), what would you mean for you to not interfere with "natural course"? Hunting in packs and not using tools? Using "natural" (meaning unprocessed) materials for constructions and clothes or maybe going naked and sleeping in trees since that's the only "natural" thing? Not taking Tylenol or aspirin when we have fever? Those are rhetorical questions, I don't want to get into natural vs. non-natural discussion.
The only question here is if this is good or bad, and for whom? There are two parts in this equation, us and animals. BTW, we are the only judges, if there was a God it would makes sense to try to follow His opinions, but since I don't believe in God I find that irrelevant.
So, is it good for us if we reintegrate endangered species and make their numbers grow? Maybe, as long as we don't have a "Jurassic Park" scenario. To me it seems like an useless effort because:
1. species disappear for a reason, for example: lost of habitat, it doesn't make sense to repopulate tigers in cities for example, or it doesn't make sense trying to repopulate Sahara with animals that need lots of water, as it doesn't make sense to repopulate polar bears if the world would be too hot for them.
2. cloned animals have no genetic diversity and would be very vulnerable to diseases and changes in environment.
3. reintroduced animals might predate on other animals or even people (tigers for example) reintroducing animals in different habitats usually damage the dynamic equilibrium of life and seems to produce more problems than it solves.
As for animals' well being? If you consider that existence is better than non-existence then it's good for the ones that are cloned -- it might not be good for other animals (if you clone lions is probably not a very happy thing for antelopes, it also might not be good for the "natural" lions if they get competition, on the other hand they would be happy to have sex with a cloned lion if they don't find a natural one

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It also depends what is your objective and your beliefs, if you believe that God(s) or The Law care about animals then you have to behave according to those beliefs, I don't so I tend to ignore that issue.
Did I touch everything that was important? Are you happy with my response?