John,
You have seemed to try and diagnose the problem well.

Try this prior to getting nervous.

Open up the rear heater valve, and the front one too.

Now, when the temp gauge starts climbing turn both heater blower's on.

If the gauge drops, this would leave me to believe that the radiator is
the culprit.

By doing this your adding more cooling area , and this means that the
radiator is partially plugged.

Simple, quick, test.