Harry when I bought my Suburban it was wild going down the road. New wheels and tires made a huge difference. The wheels on it when I bought it were all bent.
With the wheels and tires it now runs down the road just fine at 70+.
My steering box has not been moved and I'm running an original type driveline, so the comparisons don't go much further.
Unless you really want to run the 292 instead of the 327, I'd skip the engine swap and look into other issues that might affect the steering, starting with the wheels, but check the steering box, the tie-rod ends and the drag link.
Partial response to your original question: The engine and transmission should be mounted at 3 points, two widely spaced at one end, and one in the middle of the vehicle on the other. It sounds like yours is wide at the front of the motor, and in the middle under the transmission.
The original motor was mounted in the middle at the front, and wide at the bell-housing. I'm wondering if the stock crossmember, that goes under the bell-housing, is still in place on your truck.
Putting a 700R4 under your truck, as it sits today, might mean moving the transmission crossmember, depending on its design.
Your existing front engine mount sounds like a race car kind of mount, that is very unlikely to work with the 292. A crossmember for motor side mounts would fix that. They are available from lots of venders.
