Bill,
I've been using the "tip it over to drain" method for decades and it works fine for me. I always do this down at the curb. I place the drain pan in the street by the curb and I roll the mower up near the street with 2 wheels on the concrete curb and 2 wheels on the lawn. I then tip the mower so that 2 wheels remain on the curb.
I usually let the mower idle for a few minutes before draining the oil so that the oil flows better. I refill with oil, mow the lawn, and then drain/refill again. That may be obsessive, but we don't change oil that often and the extra cost and effort is really rather minimal.
My first mower was a cheaps generic model with a B&S engine. It lasted
25 years with oil changes once per year and the engine looked fine when I tore it down before tossing it in the trash. I needed/wanted a better mower with self-propel since my 11 year-old son was starting a mowing business. Otherwise, I probably could have gotten another decade out of the old mower. (Note: I changed the oil once per month during the first year. See comments below about break-in.)
If we still had 4 cycle engines on our main mowers, then I'd be changing oil at least once a month since the son is mowing about 10 lawns per week now. I switched to 2 cycle engines, so obviously we aren't concerned with oil changes anymore. We do have 2 backup mowers which seldom get used and they get the "tip it over to drain" treatment every fall, even if they haven't been used all season.
By the way, if your engine is well broken-in, consider a switch to "Mobile 1" or a similar high quality synthetic motor oil. I would consider the mower to be broken-in at the end of one mowing season, assuming that you are mowing at least once per week throughout that season. Likewise, if you are very concerned about optimal treatment of the engine, then you should consider adding a ounce or so of "Tufoil" along with the "Mobile 1". But only after the engine has been properly broken-in. Tufoil contains extremely fine PTFE particles (ie, "Teflon" particles) plus soluble molybdenum and is considered the best engine oil additive by many serious DIY types. Cheap PTFE additives have poor quality control and may contain poorer grades of PTFE (all "Teflon" is not the same) and improper particle sizes.
Also, if this is a new mower, then change oil frequently during the first season. There is no filter on a typical push mower engine and the engine produces a lot of very fine metal filings when it is going through the break-in period. This is a normal and necessary process, but it is important to minimize subsequent damage which can be caused by those fine metal particles. Draining and replacing the oil frequently during the break-in period is the only way to prevent the damage from this debris.
Good luck, Gideon
PS: Most advise that I have listed above is also applicable for auto engines, although I've had poor luck tipping the minivan over at the curb to drain the oil. But I'm still trying. :)
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Bill