Even without the vibration, bin the wankli's.
Thing is, if the inner rim is buckled or bent out of round in any way, the new tyres will vibrate too, and the inperfections will wear the new tyre out of round. So even if the rim is then repaired or replaced, you'll still get a vibration if those tyres are re fitted, as they won't be round either. I have that t shirt.(obviously there is a time factor though)
We found a few dings on another members car in this thread he didn't know he had, and one tyre was split in 3 places, all on the inside rim/sidewall of various wheels. Mot missed the badly split tyre completely.
I have had wheels balanced and checked for damage that has been missed completely "Yeah that's alright mate, you'll have no trouble with them" only to find a vibration on the first motorway.
Jack each corner yourself and spin each wheel in turn. Get under there, with car on stands. Use anything as a gauge against the rim (a cordless drill is perfect) just go give a reference and highlight any wobbles, if you like. But any out of round, dings or ossalations will be visible, and will give a vibration no matter how well balanced the wheel is.
Then do the same with the tyres, check each one for roundness, ossalations, damage, bulges, splits, cuts or foreign objects.
Once your certain your new tyres won't be worn unevenly or affected by the rims, then fit new tyres, but it would be ideal to find the definate fault before doing anything, so you know your spending money in the right area.