Well, you can actually still get new tie-rods from FieroStore.com , in case your replacements don't work out.

Worn tie-rods would cause that sensation you are getting, real soft struts could possibly cause it also due to bump-steer.

Pre-88 Fieros suffered from bump steer due to the rear suspension design, as the suspension moved up and down the rear wheel would actually turn a bit side-to-side.

I believe Horizontal play would be tie-rods, vertical play would be the rear balljoint. If your wheel has play but the spindle its mounted on isn't moving, you may need bearings.

Also of significant importance is the rear alignment and tire pressure, you can get same very odd handling issues with uneven tire pressure or a misaligned rear-end.

After replacing the tie-rods you technically should get the car aligned.

I'll have to find some pictures of the earlier suspension to re-familiarize myself with it.

Yeah,exactly,really does it when you step on gas,quickly.What conditon are your rear tie rods,ball joints in?,or have you had a 4 wheel alignment done?