I'd bet you $10 the valve guides are the #1 cause of the smoke, and $5 that the damaged bore has more to do with it...
That said: if the engine is running unevenly, like from ignition timing not being equal on the 2 sets of points, or from a weak coil on its 2 cylinders, this will make the chains very noisy. Bear in mind the Hy-vo primary chain in this engine is only 2mm from the upper engine case, and when the engine is uneven in running and the chain has a little slack, it hits the case, right behind the cylinders, and often sounds like a cam chain.
The tensioner: those parts should be coming out intact. It might be broken? I'm not quite sure, from your description, of which parts you are removing, there?
Here's the "numbers" you need to know, as your Clymer/Chilton manual either does not have them, or it has them wrong:
Pistons: the piston-to-bore clearance is 0.0006"-0.0010" max, new pistons. This engine is considered to be seriously worn when the clearance is more than 0.0022" in this tiny bore size.
Valve stem clearances: the intake must not be more than 0.0022" of "wiggle" at the edge of the valve face when it is lifted 5mm from the seat. For the exhaust side this number is 0.0032" of "wiggle" back-and-forth, toward the front-back of the engine. These numbers figure out to stem-to-guide clearances of 0.0020" intake and 0.0028", respectively. If they are more than this, it is impossible for the valve seals to stop oil from sneaking past them, into the chambers. They must be "extremely tight" in the terms of car-engine builders.
You can get oversized pistons: even CI makes sets in 0.5mm and 1.0mm oversize, or there is a "big bore" kit of 390-ish cc size out there, too. Be SURE to get cast pistons, not forged types, or you will suffer many other trials that you probably don't want to see...also, check the O-rings in those carb hose castings where they bolt to the head. Most are hard like plastic now, and don't seal at all against the vacuum needed for the carbs. This makes the cylinders run alternately too rich and too lean, in alternate firing order, which will make you chase your tail trying to debug! Also, make sure the mainjets in the carbs are no larger than #78 size (most are #75), despite what the internet gurus are trying to tell you about this bike. It is, after all, a weed-whacker-size engine, so it takes almost nothing to over-fuel it! Even having too-deep float bowls in the carbs will make this one have black, sooty sparkplugs.
...and if that's not intimidating, remember than Honda also made the engine in 250cc size, and a smaller version of it in 125cc to boot (that latter one had 2 cams, though, so it doesn't really count...).