WEIGHT
I %100 agree with Greg that you CAN easily cast beadheads with a tenkara rod. FWIW, I don't find dry dropper setups (much easier to cast than weighted streamers) to be either difficult to cast delicately with a tenkara rod, or any real stretch of the tenkara paradigm either. But I have MANY times cast (and caught dozens of 15"+ fish) on heavy(ish) beadhead wolley buggers (up to size 8) just fine with my 12' Iwana. You just need to adjust your stroke accordingly and accept that the cast is not going to be a classic tenkara delicate presentation. With those flies it really isn't with a regular fly rod either – nor does it need to be. You also need to know what you are doing a bit, or you may (as a novice) crack you tip by hitting it with the bead. FWIW fishing beadhead streamers on a tenkra rod, especially if you can see the fish, is a total blast! But I do realize this is not strictly tenkara-style delicate presentation fishing. The next step may be to hook on some bait. LOL But it is a hoot.
LENGTH
If you need/want a little extra extra distance it is entirely assessable with a tenkara rod – though you will certainly eventually stretch the tenkara paradigm. At some point you will be using a tenkara rod outside of it optimal design specs. But out to 30' (line, not total distance) you can cast 'normally' if you practice. Out this distance the main inconvenience is having to land the fish by hand-lining – unless you are fortunate to have a nice soft fish-friendly bank you can use. As I think I have posted before on here, that distance is no intrinsic problem. I have (for example) a 25 furled tenkara line that casts easily and if you add a traditional tapered 10 ft trout leader it works passably well out to 35 feet from the tip of the rod. I'd highly recommend the tapered lines for longer casts. You can even use long 16-20' mono tapered 12lb tarpon or bonefish leaders (less than $10) for an entire tenkara line (for dries especially). Those are cheaper than most of the fancier stuff sold as tenkara lines.
I have played with using "real" fly line material for the extra weight and sometime for the floating properties. For example the line that comes with the Patagonia "tenkara" setup is just a very thin (though not by tenkara standards) coated level line. But when you start casting for more distance or using heavier line you are looking at more of a casting taper and you first strain and then break the tenkara model. That is fine if it works for you, but you do eventually loose the presentation advantages that tenkara can have over other types of fly fishing.
There are also line management issues for handling a 30+ foot line. These can be solved through experience and practice. If you are willing to use a heavier line you can learn to handle easily a line 4X or more the length of the rod. I do this all the time when I am spey casting with a "regular" fly rod. This is a style of fly fishing where 35 feet or more (up to even 60+ feet for a long rod) of line is out of the tip before the cast starts. I usually am doing this for this for salmon or steelhead. On my 13' spey rod for example there is 45' out the tip), but recently I have done this for trout on light line single-handed rods and it is a blast, and I have no doubt that by constructing the right line you could manage a single spey or snake roll style cast (of a sort) with a tenkara rod. The rod action might be pretty "off", but I'm sure it would be doable with some adjustments. That would solve the back casting room problem as well for you – at the cost of heavily messing with the presentation style. But perfectly fishable. Here the problem is that it is hard to vary the distance you fish at with using a SINGLE line very effectively for lines longer than about 2X the length of the rod. But casting is NOT an issue – though I suppose a bit of skill might be initially. Listen carefully for the rumbles in the distance – that is the old-time tenkara masters rolling in their graves. On the other hand, I have seen videos of some Japanese fisherman fishing with very long fixed lines (on long rods) and doing what is in effect a vertical snap T cast (aka as a "catch cast") on small HOOKED FISH, and flipping them back 40 or more feet out of the water and straight into their waiting nets. LOL Nice trick!
OTHER UL STRATS
Of course at some point, possibly well before the point described above, this adaptation to longer lenghts gets ridiculous. If weight is the issue, a 3-weight fly rod weighs about the same or less than any tenkara rod. My 5 wt Helios 2 rod weighs less than my Iwana. If you begrudge the weight of a reel, and since you only need one under such conditions to hold the line, leave the reel at home, learn how to do do some basic fly casting (an afternoon's work), and bring a regular fly rod – maybe a cheapo 2 or 3 weight, 4 piece rod. You can now loose some of the length of the rod as well since you don't need it. Use a 7 11/2 ft 2 wt rod, for example. Get a matching single taper weight forward floating line which will weigh only a few oz. These usually are 80+ feet, so just cut off the back say 30-40 feet (or whatever) of shooting line, nail knot a loop in the back end, and attach a tiny micro-biner on to that. Clip that onto your belt loop and now you have a setup that is as light as a tenkara setup and you can cast and fish it exactly like a regular fly rod (just without the reel). Strip the line onto the water or bank, cast and shoot. You should be able to shoot line out to 40' or so after a few hours of practice on grass, though perhaps not too gracefully until you get better. But when you have mastered this you can cast however far you want. It has the advantage also that you can strip in the fish for a rod buffered landing.
Or you could get cheapo a UL plastic reel (and maybe drill more holes in it). Or make a line holder from scratch. There are definitely some DIY projects in there. I'd love to see some reports.
But just in case you are starting to think I'm totally mental, when I fish with a tenkara rod I prefer to fish a line no more than 1 1/2 times the length of the rod and agree with traditional tenkara style aesthetics – within reason. But I do carry a 25' foot line with me, even backpacking. I also like the limitations. I even like the one-fly limitations, especially with trad tenkara flies which are very adaptable as to how they are fished. On the other hand some days my mood it to see how MANY different flies I can catch fish on, and even then I don't find fishing western flies of all types to strain the tenkara paradigm too much….but is is also sometimes fun to figure out how to stretch things to the max. Maybe I will post how to construct a (oxymoronic) tenkara spey line if I figure it out. Can't wait to try my first perry poke with my iwana. LOL