It's been a while but I'm willing to take a stab at what I think is wrong. I would first suspect the display driver chips before the display LEDs themselves. If the LEDs are "burned out" due to excessive current then something in the display electronics had to fail to allow that.
As I remember, to reduce the parts count, the display driver strobes through each LED display with "ripple blanking" one side of the LED to turn on and off each element very quickly with the other side being fed with the proper character for it. That's why if you look at a classic calculator display that has been video taped, it will have a flickering pattern as it beats with the 30 Hz of the video scan.
If you are getting dimly lit LEDs or 'ghost' elements, that implies that the display switching is allowing leakage current to partially turn on elements that are suppose to be off. Again, I would suspect the drivers before the display elements though I could be wrong.
I don't know how the driver chips are wired with relation to display so I can't say how easy it is to repair. I do remember that the driver chips are custom HP parts and I doubt that there is a third-party source for replacements. Where the display chips sealed in epoxy? I also seem to remember how the display worked in the classic calculators being discussed in an old HP or PPC article.
Finally, I have an HP-55 that I bought new back in 1974 and I remember being very curious about how the display worked and why it was so bright. I was surprised to learn that there are lenses in front of each LED 7-segment display to enlarge them. In reality they are much smaller and even brighter than they appear in the calculator.
Amazing.
Gerry