I have not had time to test warrior out after the new change so I'm assuming they still can't magically generate high threat without attacking, but I would say building Agility now on tanky warriors is now even better. Since you build strength, you will need agility to make sure you are able to hit things. I'm surprised to hear you have to have to rely on other champions since warriors never had a problem doing damage so I'm assuming you can't hit anything because your agility is too low or you are not using offensive skills and went full support tank. If the latter is true then I would recommend choosing between going a more damage-focused tank since it's the best way to make use of your passive or doing what TheShepard recommended and using summons, but at that point you better off switching roles to white mage since warriors passive becomes pretty useless.
An example a tanky warrior build would-be Great heal, cleave, eviscerate, Bull Rush, whatever Ult you want. Have heavy armor, and I think heavy weapons also help you generate threat.