Chances are very high that the valves are leaking and it needs at least a step-bore and you can get genuine Honda cam chain tensioner and chain parts from either Sound Sound Honda or JTMarks at eBay. When you talk with your "reputable shop", ask them one VERY pointed question: "What piston clearance will you use?". If they tell you anything more than 0.001" (that's one thousandths of an inch - it should actually be less than that...), then go find another shop, or you WILL end up right where you are now in less than 5000 miles, if that far. Almost half of the engines I receive for rebuild now were butchered by some "reputable shop" or another - which is why I wrote that book that MauiK3 mentioned. 
When you quote 1" thou clearance is that the total, 0.5" thou per side or 1" thou per side?
1 thousandths, total. No more.
When I rebuilt my 750 in 2013 I set this at 0.0006" piston clearance, partly because I wanted to see what it would do, and partly because I am sure it won't cause trouble. In the end, my machine shop was real nervous about it until i pointed out that I have been using 0.0004"-0.0006" (like Honda does) on the singles (CB100/125 and CB160 twins). In the end they made me declare that I won't 'hold them responsible' for what happens: so, after the bike runs amazingly cooler, smoother, and has a lot more power than i expected, even when hot, I told them they culdn't take credit for it, either...
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Now, they bore their racing engines with 40% less clearance than they used to, too. they are mostly a racing enterprise, but they do good precision work.
When I got mine broken in, it had so much more power that I geared it up another tooth, to a 19T countersprocket, to drop the engine RPM at 80-90 MPH (that's normal interstate speeds out here in the West). It's really nice out on the open road!