Skier Bob, How Carefully Were The Tires Checked?
Was the car checked for defective Tire(s)? The tires need to be checked for radial and lateral run-out in case a belt has shifted. Usually this can be noticed at low speed and one can feel the car moving ever so slightly from side to side.
The wheel rims need to be checked for being “true”. A slightly bent rim will cause shaking and shimmy.
Balancing won’t remedy a situation as described involving faulty tire or rims.
Worn out struts will magnify any imperfections in the suspension/steering system.
Has the harmonic balancer on the engine been checked? The “worse going uphill (under engine load)” makes this a possible candidate.
CSA