You would be better served by monitoring those addresses yourself, directly from the blockchain, therefore, bitcoin-core is for you. Unfortunately, bitcoin-core doesn't give you (yet) the advantage of generating addresses from a single set of Seed words. However, Bitcoin-core does allow you to generate thousands of addresses - the draw-back is that they are just random - so you have to make a backup of all the private keys - which is not that bad, if you are disciplined enough...
Actually, Bitcoin Core starting from 0.13 is a HD wallet. It doesn't support HD mnemorics so its just a string of letters. You do have to back it up if you encrypt, unencrypt or change the password of the wallet. Otherwise, a backup of wallet.dat will suffice.
Rather than manually copying the addresses, you can find a plugin which allows you to insert your master public key. This will allow the plugin to automatically rotate the addresses while keeping your masterprivatekey secure.