It's called "death wobble" and most of us have experienced it at one time or another. It can become so bad the front of the starts bouncing off the road surface, like a lowrider, but somehow not as cool
It's generally a combination of a whole lot of little things. ANY play anywhere in the front end might be enough to start it, so check everything - Wheelbearing tightness, ball joints, panhard rod bushes, shock bushes/condition.
Also, swivel seals act as dampers on the steering- If they're worn, it will be easier to trigger.
It's unlikely it's being caused by out of round tyres. If the front iend is working properly, an out of round tyre should give steering shimmy, but no more - certainly not death wobble.
As an example - a mate runs a WT SWB with offset beadlocked rims and Q78 swampers, unbalanced. It has no steering damper. It's never deathwobbled at any speed until he put stock tyres back on it.
I've never had death wobble with my flogged old Q78's on my sierra, but another mate tried them on his SWB and it deathwobbled like a fiend.
Like I said - it's likely to be a lot of little things. Make sure all front end stuff is to spec.
Steve.