Paul in case you are interested in a Floating Tenkara line with a taper, Blue Ribbon Flies - Craig Mathews and Yvon Chouinard working together- have developed a couple of Floating Tenkara Lines made out of the Sage Quiet Taper, double taper, 000 size fly line, which makes up into a 20 and a 15 foot long set of floating T-lines. The price is about the same as Rio's PowerFlex Shooting/Running Line, which isn't bad considering the Quite Taper was a 70.00 dollar or so line to begin with. Rigs Floating Tenkara line is a level line except for the mono transition section at the tip or tippet end of the line. They recommend using 6:4 and 7:3 or faster rods with their Floating Tenkara lines, which may narrow down which rods to start with for you some. And, by the way, Rigs Fly Shop is an authorized Tenkara USA Dealer. I believe Rigs longest Floating T-line is now 13 feet, mine was a 12 footer but some of that length was made up of the braided line to lillian connecting line and the mono tip section of the line, both of which they have slightly redesigned since I bought my line from them.
With T-rods you are not casting a lot of line in the first place, so I don't see the taper (in and of itself) as being all that important to the casting function like it is with western fly rods and lines. For instance, I took a 3rd generation TUSA Kevlar line and glued a spot solid at the 7 feet up from the tip end of the line, and let it set up. Then I cut the line there and tied a Perfect loop in each end of the cut lines so that I could have a 7 foot long line or a looped back on 10 foot long line again. And it cast fine either way. Another thing I tried was reversing the furled line on the rod at both lengths to make a weight forward line to cast better under really windy conditions. And again the line cast well reversed in either length on my 12 foot Iwana and 13.5 foot long Amago Rods, but it required a short fast tapered FC section to keep the 5X tippet from hinging with wind resistant flies in the reversed line position.
Generally tapers go from thick to thin or thin to thick and down to thin again. In the beginning I stayed away from level lines because of bad past experiences I had with them in Western fly fishing. But I gave a level line a try after buying 12, 15 and 20 test FC leader material to replace the Amnesia I had been using for Hand-Tied Tapered Tenkara lines and it was a real eye opener. Level FC lines work much better on Tenkara rods than level floating fly lines work on Western fly rods. So if you have not tried using level lines because of a past Western fly fishing bias against level lines, do not be afraid to give a level FC line a try. I believe you will be pleasantly surprised with the level of performance and efficiency you will get out of the level Fluorocarbon Tenkara lines.
The only disadvantage I can see to putting a permanent loop or a knot in the lillian is that you can not separate the tip segment of the rod from the one below it with out untying the knot or cutting the loop off the lillian for drying and/or cleaning a rod. But the tip sections on most T-rods are solid, so I don't see it as being that big of an issue.
On the matter of Amnesia and colored mono, be it FC or Nylon, it just makes line handling easier when you can see the line to grab it.
You are getting a lot more winter back there than we have had out here. I am running out of snow to ski on. And here on the valley floor, spring has already sprung. I haven't gotten my fishing license yet, but it won't be too long before I do. It will still be a while before trout season opens but there will be bluegill, bass and American Shad hitting before too long. I still use Western tackle for the shad fishing and float tubing, where I need sinking lines and the fish can be a bit much for Tenkara....Golden.