My mate had a chuckle at this, in a positive way, and respects you for putting your opinion across as I do, my mate works on nothing but lubrication systems for cars for major performance car makers, including for for the engine mentioned, the "filling" of the tappet is done when cold at start up if it has lost pressure overnight in the tappet, and at the cold temperature before the engine has warmed up the oil is EXACTLY THE SAME VISCOSITY, whether it is a 10W30 or a 10W40, the first number denotes cold 37C viscosity, so there is no difference, the only difference is when hot around 100-120C, oil temp, where the 40 weight is that bit thicker and will help to hold oil pressure better, though a 30 weight on this engine should be fine, if all ok.
The oil is 100% NOT going to cause the tappets to stick, if it could cause these issues by being so far out tappets would be the least of your trouble.
The tappet merely contains 2 sliding "tubes" with a spring in them, oil enters the "tubes" via a oilway around the bore the tappet slides up/down in, then as oil is basically incompressible this 2 part tube type affair lengthens to fill the space between the valve head and the underside of the bucket, so setting your gap, or not as they are in constant light contact, the tiny spring inside pushes a ball against a hole stopping the oil from getting out, hence why they should be quiet when restarted next day, but as we know with a few miles can de pressurise a bit and so need refilling.
The tappets are not hydraulic in this case, so there's no argument, no manufacturer develops any engine to run on a specific oil, despite what they might say, thinner oils came in use due to tighter machine tolerances, for better emissions and mpg primarily.
The oil used whatever the viscosity has a range at which it operates best, a 10W40 covers the entire range that a 30 weight does, but when at the hot extreme is slightly thicker, but no where near as thick as the 30 weight is when the 30 weight is cold for example.
In different countries the recommendation changes despite the engine being identical in every way, so using a 40 weight in a 30 weight engine causes no harm, it just gives a bit of extra lee way when really hot as it doesn't thin out as much, but isn't needed, as the engine oil getting that hot in this country.
It won't do a thing using a 40 weight oil, other than cause it to be slightly thicker when cold, but in the temps we see in the uk it's not a issue, the poor old cossie was given a 40 weight oil by ford which will promptly kill engines if driven hard enough, it will simply get too thin, but was a good selling point and helped official mpg tests when done on the cars prior to release.
Years ago different oils were used summer and winter for best effect, despite being designed to use a certain grade.
Of a lot more importance is the depletion of ZDDP in oil, as this offers much needed scuff resistance.
tabetha