I took an advanced printing workshop last fall from Howard Bond, a noted teacher and master photographer/printer. He uses Ilford paper and teaches a simple flashing technique for burned highlights. Here is information from my notes.
Dim down small 7-1/2 watt night light bulb. This can be done with a rheostat or electrical tape over a portion of the bulb. Dim the bulb brightness down so the threshold exposure is say 10 seconds.
Make a mask for the area you want to reduce the contrast for by cutting out the shape on a thin piece of cardboard such as the material normally furnished with enlarging paper in the wrapper. Simply put the cardboard in your easel, project the image on the cardboard, and draw a pencil line, then cut the shape with a razor blade.
Now, mask out the area of the print that needs normal contrast treatment, and flash the problem area to 2/3 of the threshold time. Move the mask around while flashing as you do when dodging and burning to soften the edges.
Your final exposure will yield less contrast in the highlighted area that was flashed.
I saw this demonstrated, but haven't tried it yet. I forget whether the highlighted area should be exposed with a lower numbered filter (say 00) as was described in a post above. This is called split printing and it can be very effective in lowering contrast when burning in highlights.
I hope this provides a starting point to give the technique a try. I believe it can be a problem solver.