It is interesting what you said about EU2000i having timing belt and no separate cylinder/cylinder head and it prompted me to check the spare parts drawings of Firman 2000 I bought three years ago, and dual fuel Firman 3200/2900 bought abut year and half ago (both were on sale at Costco).
It prompted me to check spare part drawings of these and interestingly both of these have a separate cylinder/cylinder heads and both are are push-rod engines!
Not saying one design is better or worse, but these are probably little more old fashion in that regard and these may have couple of more moving parts to wear VS. timing belt wear.
Obviously these were whole lot cheaper than Honda's, but they seem like very well made small inverter generators and have performed flawlessly so far, but only time will show their longevity?
View attachment 847236
Item 54, push rod:
View attachment 847237