Evan,
As you have the timing cover off, check that you have the timing gears on the correct side. For some weird reason, Mr Douglas referred to parts as left or right hand as you sit on the bike - except for the engine, in which case the parts are handed as you look at the timing cover. With this in mind, check that the cam gear marked LH is actually on the right hand side of the bike. The cam gears look the same, but one has the keyway in line with a tooth, and the other has the keyway between two teeth. The common sense solution would have been to make both gears the same and then move the keyway on one of the camshafts - then it couldn't be put together wrong!
Whilst you may have had the carbs refurbished, you may still need to make more adjustments due to the differences between 1950's petrol and our modern chemical concoctions. Here in the UK, we have to use unleaded fuel, and I have found our bikes respond better with a slightly smaller cutaway on the carb slide, along with an increase in main jet size by 10 - then compensate by lowering the needle if the engine runs rich at half throttle.
Having said this, if you are new to 'Douglas', the perceived poor performance may be down to your riding style - Douglas engines are not like most other 1950's engines - they are not sloggers, they like to be revved. I made the same mistake when I first got my Dragonfly - it seemed 55mph was it's limit - until experienced Doulas owners told me to rev it more. With it geared the same as a Mark 3 Sports, it will go to about 58 in second, just over 75 in third, but only just manages to maintain 70 in top gear.
Getting back to the timing gears, providing the teeth are not undercut, I wouldn't worry too much about the backlash - mechanical noise seems to be a feature of the postwar engines. Camshaft wear can be a problem, but seems to be more prevalent on Dragonflies than Marks.
Moving on to the rocker arms - there were 2 types for the postwar T35 engines. The original T35's (the Mark 1's)had deeper combustion chambers than subsequent Mark 3 -5 engines. The deeper combustion chambers had the valves set at a wider angle, so the rocker arm geometry is different (enough to cause the problem you have mentioned, but difficult to see with the naked eye).
Hope some of this helps,
Regards,
Eddie.