Jim.
To take things from the top.
IT IS A LAWNMOWER ENGINE
IT IS A VERTICAL SHAFT LAWNMOWER ENGINE
IT IS THE CHEAPEST ENGINE IT IS POSSIBLE TO MAKE
You are stressing about nothing
The engine has an expected life of around 1000 hours as does the hydros
Half of the mowers out there will never get an oil change for their entire life.
The engines are cheap because the precision is very low even by automotive standards.
The engines are lazy ( 4500 rpm ceiling ) low reving with an extremely low power to displacement ratio.
Thus you can toss out most of what you know about engines & engine maintenance as it is overkill with a capital O .
Now FWIW I run all new engines that I fit with plain old SAE 30 mower oil because it is higher zinc than most car oils and contains a lot more anti corrosion addatives than every car oil.
They get between 1 & 2 hours of break in ( well I got to mow my own grass ) after which I do an oil & filter change then hand the mower back to the customer.
I give them a free in warranty service at 50 hours ( no labour charge ) and about 1/3 actually bring them back for it.
About 1/2 the mowers I service come in with the oil lower than the minimum mark on the dip stick .
Now that Honda have exited the mower engine market there are no high precision mower engines left in the market.
If you want to frighten yourself download the IPL for your engine and look at what parts are in there, or to be more precise what parts you would have expected to be in there that are missing .
All mower engines are built to a price, not a quality standard.
If you think I am talking through my anal cavity then look at the difference between the prices of Horizontal crank engines and vertical shaft engines.
The former are nearly twice the price because twice the engineering goes into them and they are expected to run around 10 times the hours that a mower engine does.
But try and find a compressor, pump or generator with an hour meter on them.
The average 500cc air cooled carburettored motorcycle engine puts out around 60 Hp
The average 500cc mower engine put out about 20 Hp.
Now FWIW you will get the best service life from your engine, if you follow your instincts and change the oil immediately after the last mow of the season.
Forget the numbers, they really are just a guide .
And to drive home how meaningless the numbers actually are, the hour meters are fitted by the mower maker, not the engine makers .
Thus on most JD's the meter records the hours that the key is in the on position , ( engine running or not ).
On Toros the meter records the hours that the PTO is on ,( engine running or not ).
Engines fitted with a tiny tach will record the hours that engine is running as they use an induction pick up on one of the HT leads.
I play with vintage & veteran motorcycles and oils are the most debated topic.
My advice about the best oil is the stuff you just took out and the more often the better .
Synthetics will not hurt a mower engine but as most of them have a lower viscosity base they are more prone to leaking , particularly when not being used .
My customers that swear by them do notice that the engine gives off some exhaust smoke when first started and this is simply oil that has leaked past the rings and gets blown into the muffler where it slowly smokes off.
I have removed mufflers to confirm this.
My personal belief is synthetics in the engine are lipstick on a pig, but if pigs wearing lipstick is you thing then go ahead.
It is your lawnmower so do what makes you feel comfortable.
There are lots of people ( including many of my customers ) who use the same oil in everything fo convienance sake and very few of them report a higher rate of failures than others who have a garage with 30 different oils in them.
The caveat on this is the one oil customers do tend to change their oils regularly.