I usually end up using a full quart when I bleed a trailer, you can use a fluid sucker to suck the old fluid out of the MC first, refill with clean, then start with the furthest rear axle and bleed it.  The forward axle should not need near as much to get clear fluid out of each bleeder as the main lines should be clear already.

My trailer tongue, at the surge actuator, has "XR84" stamped to it.

Search shows the replacement part for the whole MC assembly (minus the metal structure) is DX44FR.

I also see a cross-ref to 054-127-22

I think the following retailers have it:

• etrailer
• brakes for trailers
• trailerandtruckparts

9 minutes ago, BlindSquirrel said:

Just looking at the fluid, it looks like it was due for replacement for sure. It turns brown whenever moisture is present. I like your method of changing it, that's how I do it automobiles, with that bleeder. Did the fluid ever turn clear in your bleeder hose? Meaning, that all the old fluid is out and the new was flowing in. I do think you are on the right track with the Master cylinder.  

It was always a bit "tea colored"

I am thinking I did not get all the fluid out. Maybe it holds a total of 16 oz?

Clean brake fluid should be clear with a slight yellow tint (almost like gasoline). 
I tend to agree, there’s possibly a sticking master cylinder causing this.  There is also a small shock absorber in the actuator assembly to help keep pressure off the cylinder at regular tow operation.  Both of those are serviceable without full actuator replacement (see my previous posts in here, should be the service manual for them). 

Check the plug sockets that the relays go into to see if you have loose connections.