How many pieces is the rod? You should only have to have one or two guides removed to get to the cork handle, if it's a four piece rod. You want to work from the top down when you ream out the new cork handle to get the best fit. Removing the reel seat is possible, but a real pain and you can easily damage the reel seat.
Is it a custom or factory rod? If it's custom, then only the blank is warrantied by Orvis.
You can contact Orvis as well, but with an older rod they will typically offer you an upgrade. That cork is pretty bad and no amount of filler is going to stay on the rod for any length of time.
The only other option would be to sand the handle down and narrow it quite a bit, but that would be my last option. You may not enjoy the rod as much if the handle is too small (narrow).