Does sound like the P/s pump, or, something binding up at the steering joints. Have they been greased? Especially if you say it gets better when warm. Before replacing the pump, might try to flush the P/S fluid with fresh and see if that helps.

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1987 300TD 147,000 miles- Palomino leather interior, 1995 facelift and body cladding, E350 wheels, Rebuilt suspension and sport springs, rebuilt turbo, New Monarch injection pump and injectors....and the list goes on and on...