It is imperative that you recap the board. The capacitors leak and will dissolve the traces near and under them. This has already started to happen, as the legs of the existing capacitors have dissolved, causing them to fall off. I would imagine you have some trace damage. Probably not completely compromised, but likely the surface has started to corrode, so look closely with magnification. I use solid polymer versions so that they will never leak again. They are more expensive, but in the long run, I say worth it.
https://www.digikey.com/product-detail/en/nichicon/PCV1D470MCL1GS/493-4369-1-ND/
One of the capacitors is a smaller part, not available in solid polymer. I use
https://www.digikey.com/product-detail/en/panasonic-electronic-components/EEE-HD1H1R0R/PCE4972CT-ND
I remove the capacitors with hot air. Protect any nearby plastics with Polyimide tape, or another heat reflective material (foil can get you by in a pinch). Practice safe ESD procedures. A wrist strap connected to the board is adequate. A fully grounded work mat is better. After removal, use desolder braid and flux to remove the old solder from the pads, then clean thoroughly with 99% alcohol. Finally, re-tin the pads before cleaning the entire board.
Just as important as recapping is making sure to clean the board of all the capacitor dielectric after removing the capacitors. You must make sure you get all of it off, especially around the UE8 area. Don't be afraid of white vinegar and a toothbrush. Rinse well with distilled water, followed by a 99% alcohol rinse. Blow dry with compressed air. Afterwords, I bake mine at 120deg for 15 minutes.
Now, install the new capacitors, taking care to note polarity. There are lots of tutorials on youtube you can watch if you've never done this before.
I would say it's pretty darn easy, especially If you have previous soldering experience. The hardest part is the removal process, which is elementary with a hot air station.
EDIT: On a side note, congrats on the DiiMo. They're pretty hard to come by these days. If you are looking to sell it, PM me!