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I found G was more forgiving when I made changes - i.e. seemed to place much more value on the existing backlinks whereas Y completely and utterly dropped the sites after a redesign.
Of course, I think my luck (or lack of) with Y could have been just not including keywords as often in content etc, I was writing it naturally without too much SEO (aside from the usual 'rules') in it.
In the past, I have kept any old content pages on the server and built a new site in the foreground so the SE doesn't see a 100% change. I don't know if that had a softening affect but it worked for those particular sites. If, as you say, this particular site only has one content page (presumably the index) you'll have no choice but to replace it.
Changes in Y SERPS seem quite infrequent (but seemingly different algos/indexes spread over a few datacenters so can look bouncy) so it can be a while before you notice any change and hopefully at least make your money back in the meantime.