Yes, you've got to take the base of the mast off to get at the internal downhaul, but it's not that big a job. To get at the bit you're after, you'll need to lower the stuff that's attached to the bolt up the mast. The way I did this was to tape a thin piece of rope end-to-end with the bolt before pulling it out of the mast. You can then pull everything out of the bottom of the mast, and when you're done, pull the rope tight again and slide the bolt back through.

I wouldn't worry too much about the knots in the rope. The problem you may have is that the cleat kills the rope by pulling the cover off. It may be that the spectra you've got now was a quick repair after this happened to the original rope.

Paul