After many months of investigation we've reached a roadblock... there's no evidence that Konami's rulings change  regarding "Rivalry of Warlords" and "Gozen Match" took effect at or before SJC Edison. Thus the responsible and prudent course of action is to apply the Upper Deck Entertainment rulings  to the cards. This change only affects the ability to Tribute Summon (not Special Summon).
Moving forward, apply these UDE rulings to Rivalry and Gozen:
If you have only 1 monster on the field face-up, you may Tribute it for a monster that is a different Type/Attribute.
If you have 2 monsters on the field face-up of the same Type/Attribute, you cannot Tribute 1 of them for another monster that is a different Type/Attribute (even "Jinzo") as you would then have 2 different Types/Attributes.