I replaced a steering box and P/S hoses in a truck a couple of years ago, and had bad air bleed issues, even though I (mostly) followed procedure for bleeding the air.
My local shop told me "new P/S pump". Turned out that the air worked itself out a couple of days later (although I eventually did have to replace the pump, but that was way later, and on my schedule).
If the system has foam, it's got too much air. When I had the air bleed issue after the replacement of the box / lines, I had filled the pump (and turned the wheel lock-to-lock) prior to starting the engine. But it only took a second for the system to suck all of the fluid out of the pump (and start whining / producing foam).
When I did the pump replacement (recently), I filled the pump reservoir to the opening. No air bleed / foam issues, and after a few minutes of running, the level had settled down where it was almost at the right spot (I remember having to add a tiny bit more, not siphoning out excess).
The Saginaw pumps are really sensitive to fluid level -- a couple of minutes without fluid can be a death sentence for them. Sometimes they'll work for awhile after being compromised. But they'll usually whine, at least part of the time, for the rest of their days.
I'd check to see if the rack / hoses have any visible leaks. While I had new fluid from having replaced all of it doing the box, lines (& hydroboost module!), it's probably possible to bleed the system via disconnecting the low-pressure return, capping off the pump orifice (with the little plugs that come with new pumps), and then letting the line bleed into a pan while you're refilling via the reservoir at the same time. You have to be quick about it, unless you've got someone to start / stop the engine, as needed.
Tip: Get a gallon-size container of P/S fluid (cheaper, vs. multiple quarts), and a smaller bottle to pour into the reservoir (I picked up a set of plastic ketchup / mustard bottles at the dollar store, which worked a treat.)