Yes, as it stands you cannot mix Office 365/2016 with earlier versions of Project.
BUT, if you read back through this question you'll see there is no need to cancel your subscription. There is an offer for a free upgrade to Project and Visio 2016 which will install alongside of Office 365/2016
You can try contacting MS support directly and if they are not already aware of the offer (many still are not!) give them the links. EVENTUALLY you will get a free license for the 2 products.
OR, you can wait to get a private message from one of the MS employees who are monitoring this question. They will also help you get the free licenses.
Either way the process seems to take several days from start to end. If you are pressed for time, there may be a way for you to back out to Office 2013.
How do I reinstall Office 2013 after an Office 2016 upgrade?
https://support.office.com/en-US/article/How-do-I-reinstall-Office-2013-after-an-Office-2016-upgrade-a6ca92f4-cbb4-4609-9fdb-f8d3dd6812f3
If that doesn't work, there is a more "manual" method I can provide documentation for.