There seem to be a number of things that might cause those symptoms, Mark. My first guess would be that the decompressor was stuck in the part-compression mode. My second would be erratic ignition.
A splash-lubricated engine has both oil and oil mist flying around all over the internal spaces, and when it has a vertical crankshaft, this can easily be made to extend to the rockers because of the splashing and surging of liquid oil, as well as mist, through any passage that exists.
Here is the valve compartment of a Honda GXV140 cylinder head. The oil feed and drain holes are circled in red:
Note that the same passages are very much larger where they pass through the crankcase: they are reduced to those small sizes just where they enter the valve compartment. Note also that the feed hole (the upper one) is somewhat larger than the surge/oil return passage (the lower one). This has the look of having been developed by trial and error, to get the desired amount of oil in that compartment.
On your small Intek, Honda's high and low oil passages must be replaced by something else that works. I don't know how much oil the little tin decompressor would fling through the hole directly beside it (on a vertical crankshaft engine), and I have no real confidence that tiny drain at the bottom of the pushrod compartment would remain un-clogged over the long haul, but your guess as to how it works sounds plausible right now. I haven't seen one of those engines so I can't look for alternative explanations. Overall, I suppose the proof of the pudding is in the eating: either the valve gear gets oiled, or it eventually shows signs of lack of lubrication.