From ASP.NET 4.6 onwards, TLS 1.2 is the default. This means if your server has been kept up to date with patches and .NET updates when they've become available, and (if required) has the necessary registry changes (see @18.2.1. Server support above) then it should make outgoing secure connections using TLS 1.2 by default. The easiest way to test this is to simply try switching the web site to ASP.NET 4.6 and then test that it works. To do this, open the web.config file (in the root of the web) and find this code:
Then reload the web site. It will take a few seconds as changes to the web.config will cause the web site code to rebuild. But you should see the web site load up and it should work exactly like it did before the change. If some page error appears, and you're sure the change you made above was done correctly, restore the original web.config file, as it seems your server does not have .NET 4.6.
You can try adding this (or check with your host if on a shared server), and then try the process above again. This avoids any code changes in Kartris.