Little River is very low right now. You will have to portage a bunch. Places that I have put in are at Perry's Mill and Coulter Bridge. The times I have floated I have taken out at the Water Treatment plant on 411 (Sevierville Rd). Once again the water is really low and this could take a very long while. You might want to consider the Holston or the lower part of the Hiwassee. Both of those rivers are tailwaters and will have water.
"The gods do not deduct from man's allotted span the hours spent in fishing." Babylonian Proverb