I might not be following you, so maybe ignore this - but if you let the bottom u-joint stay on the rack when you take the old rack off, in other words disengage the u-joint from the steering shaft, not from the rack, you can then swap the u-joint onto the new rack on a bench or a table where you have more control over the process.
Installation of the rack is easier also - the u-joint is already mounted on the rack - that connection between the u-joint and the steering shaft is easier to make than the connection between the rack and the u-joint.
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