A few years ago I was in a similar situation, when Google moved the framework from 2.0 to 4.0 - but my software was closely tied to SharePoint v3 (2007) which is .NET 2.0.
To stay on .NET 4.0 you have a few options:
- Stop using the library, and add webservice references in Visual Studio directly. VS will study the webservices itself and come up with something. So you'll miss all the library stuff like ReportUtilities but at least you got something workable.
- Build your own version of the library.
I did the second. I downloaded the sources of the library from the OLD framework. Then I downloaded the sources of the next version, on the newer framework. I compared all sources and made up my own library, which essentially was the old library plus handpicked improvements of the new library.
After that, I downloaded the sources of the oldest version of the library that was supporting a newer AdWords API. I compared those sources with the sources of what I call "next version" above, and applied the changes to my library. Then I had a library supporting a newer version.
This method only works when the library developers don't apply very big changes. It bought me 18 months (!) and then we were finally ready to move to the newer .NET version. You probably have less time because the library developers are trying to have the library support .NET Core and other things, which implies big changes.
Oh, one more thing: On 2 October v201609 will not completely disappear. It will keep working, but every now and then you get a sunset error. If you retry you may get the right answer. This works for another few days, maybe weeks. Disclaimer: this was the behavior about 2-3 years ago, I don't know if it's still the case and I can't predict how Google will handle this on October 2 and onwards.