I don't really like the UNLICENSE, because I am not 100% convinced that that license does exactly what was intended in jurisdictions that don't allow you to dedicate your work into the public domain1.
The MIT license explicitly allow sublicensing of the work, so my recommendation would be to go that route. Then you can, in the file that you borrowed from ...
The rules are very simple: If you want to relicense a project, then you need approval from all the copyright holders.
It does not matter here that the MIT license is mostly a subset of the Apache license. They are different licenses and if you want to change the license under which the project is offered, you need permission.