Maybe it just makes better sense to have a "proper print washer" ...;)
I tend to think that Thomas may have a point in his question about stop bath.
I once also had problems with brown spots (dektol and Kodak Polykontrast FB) but disappeared when I was more carefull with a proper stop bath using for 1 minute.
I suppose you are not using selenium toner because you didn't mention it, but brown stains after selenium is an indication of residual silver on the print due to inadequate fixing.
The rational for using concentrated fix for RC prints is rather meaningless as the support does not suck up fixer, and the emulsion is fixed when it is fixed and thus can wash out in short or long times depending on concentration.
HOWEVER, the argument fails when we get to FB paper. There is an affinity between the fibers and the Baryta subbing for Hypo and Silver Hypo salts and this means that you can require much longer times for FB paper if you use concentrated fixer. I suggest that in this case, you follow the manufacturers recommendations.
In general, extended wet times with RC are not a good thing, since they increase the risk of edge separation and internal contamination. Variable wet times - which is what you get when you gradually accumulate prints in the rinse tray as you go - mean the different prints are seeing different conditions and make it more difficult to troubleshoot.
Interestingly, it wasn't safe to do that with Kodak RC papers. In my own tests, Ilford RC papers have consistently cleared in about 15 seconds with fresh film-strength rapid fixer, making the 30-second recommended fix time reasonable. OTOH, Kodak RC papers often needed longer, which explains why Kodak used to advise a longer fix. I wonder what it was about the formulation of the emulsion that was responsible for that difference. They also advised a longer wash, which raises its own questions and complications.
I've had what looked like rust colored dots on fiber prints when I lived in california. These were selenium toned. Usually I didn't see the one or two spots in a print until they were coming out of the final wash. I never figured out what caused it.
I admit that I am quite sloppy about stop bath. I use it until it is quite tired and almost never stop for a full 30 seconds.
Perfect practice makes perfect.