[COLOR="Blue"]Is there a reason not to replace the capacitors?[/COLOR]
Not that I can think of.
You will probably not be able to get a schematic of the board so I would just replace all the electrolytics on the board.
I do not know which ones are for the display.
With luck perhaps someone else will jump in who has this knowledge.

Followup - I purchased the 10 capacitors from Electronics Supply in KC for $14.58. Installed them, the display looks fresh and bright.
I would not recommend this repair to anyone that doesn't have circuit board soldering experience. The copper circuits on the board are extremely thin and will lift with little heat. I had to splice one I messed up while trying to get the old part off. It doesn't appear to have been designed for repair. I took the display to the parts house so I could compare the physical sizes of the offered replacements. The replacement 3300 ufd was slightly larger in diameter and interfered with other parts placement but I was able to work around it.
The board is relatively easy to get to - just two screws from the bottom of the panel. However, there is a multitude of connectors and single wire connections. Make a drawing of the locations and wire colors - you can't remember where they all go without it. You have to lay the front exterior panel in the opening to remove the display. Lay a heavy clothe across the entry or you will wind up with a scratched exterior panel. The work is not to difficult but tedious and you have to get the circuit board partially out of the case and then bend it back for access to the solder side. Again, I don't recommend anyone doing this repair if they don't have circuit board experience. Otherwise, you will have a board that even the Internet $99 repair shops can't fix.