Heavy shake in steering wheel related to rpm or load--intermittant Options

[slo8012]

I am posting this here, but it may belong somewhere else..if so I apologize.

I have a 1995 GT hatchback automatic that has an intermittent steering wheel shake at times on the highway. It happens sometimes when I am cruising at about 80mph and either release cruise control or back off the gas because of traffic ahead. I notice some vibration in the steering wheel, and if I give it slight throttle (2-3k rpms @60-65mph) the wheel will shake violently and pull to the left. If I give it more gas (5k rpms) the shaking becomes a vibration and calms down somewhat. If I stop, the problem goes away for a while but comes back intermittently.

I replaced the struts 2 years ago, and had the timing belt replaced last year.

I have had the tires rotated and balanced.
I have had the brakes inspected, and while I need new front brake pads and rotors, the rotors are not blued or warped and the pistons are operating normally.
I have had it jacked up and all the suspension components feel tight, nothing is loose.
There is a little play in the driver's side axle coming out of the transmission both in and out and radially, but I still have all my transmission fluid and it is not discolored.

Right now it is sitting at a dealership, and they say that all 4 motor mounts are bad, with aprox $1k to fix it from them. Add this to the $300 brake job and I might be looking to sell my car instead. The paint is failed and there are dings in every corner.

1) First of all, could bad motor mounts cause this problem?

2) Is changing the motor mounts something that a reasonably mechanical (not expert) person like me could do? (I have changed all four struts and followed one of the CAI postings on here to replace my intake with bent mandrel tubing, but I doubt that I could handle an engine swap or turbo installation)

3) if it is not the motor mounts, what can I do if the dealer can't make the problem happen while they are driving, or what else can I investigate to solve the problem?

Thank you,

Derek

[RabidTRD]

The mounts are cheap and not very hard to replace. Only the rear one is the hard one and I forget who, but someone on here replaced it super quick and took a video. $1000 is them insulting you honestly. Tell them to f-off and go find a real shop.