Did you set the valve clearance with the crankshaft just past top dead center, at the end of the compression stroke? People sometimes have trouble adjusting valve clearance with Briggs & Stratton engines due to the Ezyspin feature, which deliberately holds the intake valve open .010" during a large part of the compression stroke. B&S do that on the principle that it eases the job of pulling the starter cord, and there isn't all that much leakage from just .010" valve lift once the engine is up to running speed. It sounds as if your Honda might perhaps have something similar, though .050" sounds rather a lot.
There is of course a possibility that the engine has a camshaft problem, either due to a manufacturing defect or through wear. I once saw a little Honda 4-stroke generator engine that stopped running, and the reason was that it no longer had any cam lobes. It doesn't sound like a highly probable explanation of your engine's problem though; it would be an odd kind of cam wear to create a bump rather than remove one.
If the compression feels OK, compared with similar Hondas, I doubt the camshaft is your problem. Bear in mind that your engine has a substantially higher compression ratio than a side valve B&S engine, so you should feel a fairly solid compression load on the starter cord. You can find out for sure by borrowing a compression gauge that fits the spark plug hole. In my experience an engine that is supposed to have 140 psi compression pressure will probably start fairly normally down to about 90 psi, but below that there may be a problem starting it. Remember that Honda specifies the 140 psi figure at 600 rpm, which is pulling fairly briskly on the cord. At lower speed, an Ezyspin-type feature might give you a much lower pressure.
