I also think a wheel is out of balance
That could easily account for the vibration.
Also check the wheels carefully - I came across one the other day on my neighbors Mercedes which were perfectly round, had 4-5 mm thread left, but there was a large area where the bottom of the thread was bulging outwards, making a patch on the wheel with almost no thread at all. This caused the car to sway at 20-30mph.
Speedo cable is fairly easy to replace (you just need an extra joint below your elbow, but what's new? :-) ) , but I remember having a tremendous problem getting it off the wheel end, as the tap had corroded.
PS: Personally I would never try to save money on tyres - 4 of the best you can find is a lot cheaper than your joy of driving, or even your life.
/Lennart