Keith

Do you have a sensor simulator? If you do try simulating the lambda switching from just after engine start-up and see if this makes a difference.
Some years ago I had a Wrangler 4.0 with similar lanmbda sensor / injector duration behavior to yours i.e. dropping to 0 volts during the initial 60-90 seconds of running. Also it was reluctant to go into closed loop.
This had a universal sensor fitted by another garage and I found that if a good signal was simulated all the issues disappeared. Fitted a genuine sensor and it started to switch within approx 20 seconds of starting and went into closed loop shortly after. HTH

Steve