I don't suppose there is any easier way? It takes days to download it all again.
There's nothing easier than just waiting a few days 
And it's also the most secure, I don't recommend messing around with private keys if you're not sure what you're doing.From your screenshot: you use 450 MB database cache. If you have enough RAM, increasing this might improve the time it takes to synchronize the entire blockchain. If you have 16 GB RAM, try for instance 4096 MB dbcache.
I might just try that. If I do, should I do it this way?
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If I had done it differently at the beginning, by replacing the wallet.dat default file with my old one, before launching the BitcoinCore and indexing, would it have worked properly? Maybe it's better I uninstall,reinstall, and do that step?
Last time I did this, I had to restart it after the first day because it crashed.