PJ, I bet that ticking is because of the build-up of some crudrestricting a piece of the valvetrain. When you first change the oil and the detergent package is at its best, it dissolves this and the ticking goes away. However, the engine wants to allow build up in that area and as the oil begins to age/weaken, the build-up returns ... as does the noise.
You might add a mild cleaner. SeaFoam was recommended above but I've never tried it. There is some info on this stuff on this site. I'd use an ounce of Schaeffer Neutra in a heartbeat. I bet it'd do the trick.
I am terribly mistrustful of OEM oils. They are high in price but analysis usually shows them to be mediocre or worse.
For the long term, try switching to a different oil. Ideal would be one of the detergent-heavy diesel/fleet oils also recommended for gas engines. These are usually 15W40, but come in 10W30 if you look hard enough (forget the mass-market stores and contact your local oil distributor instead).
I'd recommend Chevron Delo400 or especially Pennzoil Long Life (which has a lot of moly). Again, the 15W40s will be easy to find but both come in 10W30 if you don't mind calling around.
I use Schaeffer 15W40 synthetic blend in nearly all my lawn & garden equipment. Works great. I even did an oil analysis on a sample taken from this engine and posted it on this site. Try searching using the words "Honda Tractor."
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Bror Jace