I've also swapped out the display on my 34401A because it was dim and uneven. I figured people that are considering doing this might be interested in seeing the results, so I made some pictures. The old display is on top, still attached to the front panel PCB, the new display is at the bottom.
I got the display from china, ebay I think. It's not an OEM part, but it matches the original. It was no trouble to replace it, except I didn't notice that the metal frame around the display made contact to one of those bent tabs holding the glass, which cause a short. After I fixed that, everything worked.
The pics are intentionally a bit dark, because I had to set the exposure settings initially, and wanted to leave enough headroom for the new, brighter display not to be blown out. In real life, the old display was quite hard to read under direct illumination, the new one's fine in that situation.