So it's been a minute since I asked the question. Thanks to all who offered ideas, and especially Stingray for providing some material for experimentation.
Ultimately, I found I had the wrong idea on how Standel did the control panel. I thought it was a colored panel engraved from the front surface to a clear substrate. Really, it is a clear panel that's engraved in reverse from the back surface, and the chassis is painted to provide the background coloring.
But I've got the clear panel made and engraved, and the LED lighting sorted out. It lights up beautifully!
I might not have looked everywhere I could, but I seemed to only find superbright blue LEDs in a round 5mm package. The acrylic panel came out to 1/8" thick. So I filed the round ends of the LEDs flat to butt against the acrylic, and also filed two opposing sides to get the LED down to a flat 1/8" thickness. The filing left the surfaces a milky white.
I arranged 6 LEDs to light from one end, wiring them in parallel using the the LEDs' own leads with some insulation off of 22ga wire to prevent shorts. 22ga wire is attached to the last LED, which runs into the chassis through a small hole, with the LEDs' dropping resistor inside the amp chassis.
In the end, the simplest way to mount the LEDs seemed best: The panel is fixed by the pots, so the flat ends of the LEDs are pressed against the panel's edge. The top and bootom of the LEDs will be held in place by the cabinet surface and chassis, since the panel edge is not exposed by the cabinet control cutout. Some thick rubber splicing tape is built up and applied to the chassis on the back end of the LEDs to keep them positioned.
The 6 LEDs are in an array less than 2" long, which might be overkill. But it seems to work well and give the desired intensity to the lettering.
Pics to follow in a few days when I get a chance to take and post them!