[alarie]

Do it from the outside! Repairing all of those inside areas will take forever-no advantage to that method unless you are rebuilding all the areas to change the layout.

Mark out your cuts and grind BEFORE you cut, as this will save a ton of time when you put it back together and you will have nice and flat areas to glass back onto. Don't worry about putting the wood back in in pieces, the strength of the laminate is in the skins, the core is just holding them apart. Most foam laminates are plenty strong and the foam is often kerfed every 1"! If you are concerned, just stagger your joints, but it is not an issue.

Follow Hammer's lead, very quick way to do it. Just leave yourself enough room at the edges so you have 3-4" left to glass onto without going around the corner (much more work, as noted by others).

Peter