I have never had much luck using a CJ on the Clinch, but your approach using a #16 or 18 BHPT should be fine though. I typically use two midge pupae and in the slow water it doesn't have any trouble getting to depth.
I highly recommend an across and down drift. In some situations, I understand an upstream approach is required. However, on the Clinch, casting across stream and allowing the fly to drift all the way down stream is my most successful approach. This is also true for the SoHo. I have been fishing beside many other fisherman, some I know and others I don't, who insist on fishing upstream. Many times I have had a 3 to 1 catch ratio over them. Now fishing in the really deep water reduces the line shyness of the fish, but it is still there. Another recommendation I would make is to use 6x fluoro or 7x mono. My strike rate is greatly increased when I use these tippet sizes. As far as indicators go, I can't say enough about the 1/2" thingamabobber sizes. I just wish I could order an entire pack of white. They are perfect for this type of fishing, and are very sensitive. Also, strikes when fishing this way are typically very subtle. Don't expect to see your entire indicator go under. Sometimes, it is just a hesitation, set the hook immediately.
As far as how to approach the deep water, I usually fish it from the side. This allows me to be standing in 12" water and casting across into 3' water. When you are in the deep slow stuff I prefer, very rarely do you have to worry about different current speeds altering your drift. Typically the drift in these slow sections is pretty uniform at the surface.
Off topic here..... Your name sounds very familiar to me. Are you from North Knoxville (Halls)?