There are other methods to attack core rot as well. If you can access the rot from below, you can also cut and replace the skin and core from underneath. The chain locker might be a good candidate for going from underneath. The aesthetics wont be an issue.
I have also heard of a method that uses a drying agent and a sealant, that is injected through a hole or holes and cures around the rotted area. This method has had some detractors, but there are some who swear by it, when done properly. Check the web for this, I have seen the postings, but dont recall the name of the product or method. You will need to drill a few holes for this, to both inject the epoxy and to fill the voids fully, but patching a few holes in the non skid, will be a lot easier than replacing the entire section.
Eric