100' of half-inch pipe is only a gallon, so then the first gallon you put in would be cold. What's your tub capacity?I have a similar situation. We have a new house and the Jaccuzzi tub is way at the other end of the house. We have a 50gal hot water heater and when the tub gets about 1/2 full the water turns cold.
For 108F water, you could do 50 gal of 120F and 15 gals of 70F water.