Power steering hard, not powered at first start up

I replaced the power steering pump on my Jeep (2001, stock PS pump and box) and now I have some issues that almost seem like a "bleed the system" problem but I'm not certain.

If the Jeep has been sitting for a while (i.e. drivetrain completely cold) when I first start the Jeep it takes a couple saws at the wheel to get the power steering to be powered versus feeling completely unpowered.

Every once in a while if I do some high speed four lane highway work along a straight portion of the highway when I pull into the off-ramp I notice that for a second or two the power steering feels slightly unpowered.

This is the second replacement pump and reservoir in the last four months;

* old, ~five year old one "exploded" in August due to being worn out, shot the pulley and shaft around the engine bay while cruising on four lane highway,
* replacement leaked fluid between the pump and reservoir so pulled it to fix, turned into spare,
* early October replacement in the meantime is Delco reman, seems tight and dry.

The symptoms occurred with both new pumps.

I've nursed the fill up of the reservoir while sawing the wheel back and forth both with weight on the front wheels and not. It's been like this for a few months now so it must have self bled itself by now on the October pump.

Better method to bleed? Maybe it's a blockage in the lines and/ or steering box?

Steering feels fine otherwise but maybe there is an issue with the recirculating part of the steering box?

The steering box is the original, 2001 that came on the Jeep AFAIK (purchased Jeep in 2003).

Any insights appreciated.

Thanks.

You should consider a new OEM unit next time around. Remans are notorious for early failure, and are a waste of time in my book. Most PS systems will bleed excess air in the first minute of driving. I doubt that trapped air is the problem.