I have an 8-man and a Sawtooth by Kifaru; both with liners. I think if you had one to see/study you could potentially make one for your Ti-Goat tipi. The key for me would be that it fits and hangs correctly with minimal or NO sag which robs internal space. You want the liner to follow the contours of the tipi 'wall' and maintain a constant space of at least 2" for air circulation. Your liner doesn't need to extend to the cone. Just get it to the 5-1/2 to 6-0 ft level. In all likelihood your tipi probably has some sort of internal webbing/loops or tie-off points at that height designed for the liner. If it doesn't have them, you'll need to add them yourself. The top of your liner needs matching ties to attach it. Same thing applies at the bottom of the liner with regards to tie loops. If everything is good, your liner will be fairly taut and follow the wall contour. To imagine what a full liner looks like, imagine your tipi with the top clipped. That's what you are creating. You'll need openings (think 'slits') for the doors. All edge-areas of the liner will be secured with ties. The liner material needs to be soft and thin (such as silnylon) and basically waterproof. Condensation drips onto the outer aspect of the liner and then runs down the liner to the bottom edge where it drips to the ground. A liner which absorbs any moisture is a definite no-no.
I personally wouldn't do my own liner unless I had a lot of time and patience, plus material and enough skill to do it correctly. I think all the tie-offs and fitment issues would give me a headache. As far as full liner vs partial, just know that any unprotected areas are going to drip or shower. If that doesn't matter, then save weight and fabric. Me...I'll take as much dry space as I can get. Never know when an extra man needs to jump in, or that dry space is useful for firewood, gear storage, etc.