If it is for short term stays, you could try to sleep radially between the poles, or use a bivi bag. The rain normally only drips down the poles, what comes through the vent is generally drizzle and should fall in a puddle between the door and fire. A tall enough liner can be snuggled under in wet weather and that will keep you pretty dry. The only other important bit is making sure the fire draws through the vent A tipi is a chiminy and it will wreck a good pair lungs very quickly if not set up right.
Your tipi is beautiful. They are the most amazing spaces.
Xylaria's advice on lining height, rain-catcher, Ozan, fires etc. Is probably some of the most informed you're likely to get.
Xylaria, what height would you go for on the lining of a 5m tipi? What do you think of ozans?
Cheers!
Huon