There is a nice Apache 2.0-licensed project that already implements the foundation of a way more elaborate product that I intend to sell as proprietary.
Something like the 70% of the code will be modified or rewritten, so it's not really like I'm including it as a module or library.
Unfortunately I cannot release the sources of the final product as OSS, but it is possible to add credits and acknowledgements.
Would this be legal?
First, a caveat. If this is critical, you should consult a lawyer and explain exactly what you're doing - this answer isn't legal advice.
What you're describing is allowed under the Apache license. You will still need to comply with the conditions such as providing attribution and including a copy of the license. The best source of information is the license itself; however, the Apache Foundation does provide a nice summary in its FAQs here: https://www.apache.org/foundation/license-faq.html#WhatDoesItMEAN
