Hi and welcome - you have gotten some great advice, but one word of caution about silk thread - unless you have wrapped a lot of other rods, I find silk very difficult to work with, and you might want to try nylon instead, and Color Preserver will keep it from disappearing.
The set in the tip can be removed relatively easily by heating some sort of microwave heating pad in the MW then wrapping the offending area with the pad, then very gently "setting" it into the proper position until it cools. You may repeat if necessary.
As far as your finish goes, I have been using Birchwood Casey Tru Oil and it is so easy to use, every time I pass by, I just wet a shop towel(lint free) with the oil and run it up and down the rod. It dries in just a couple of hours, so can be repeated often. You do need about 12 coats, and a light scuffing with a 3M pad every 3-4 coats, but it is almost trouble-free.
As to your grip, you might consider re-shaping the present grip as though you were building it from scratch.
Good luck and have fun.