Just 系（けい） does the trick. (Learned this one from a friend with an ancestrally Mexican but American-born husband.)
E.g. メキシコ系, イギリス系, イタリア系
Now I'm not familiar with 日系, but the dictionary suggests it means an ancestral Japanese person who isn't a Japanese citizen. Is that incorrect?
My understanding of 中華 is that it means "Chinese food", so I wouldn't think that would be the right term to use, but maybe someone else can clarify. I think 中国系 should be good, though, following the same pattern as above.
I got 日系アメリカ人 from a textbook. Chances are it is correct. It is supposed to mean Japanese American which refers to American people of Japanese descent.
I don't think 中国系 is correct because 中国 refers to China, not ancestry.
中華系シンガポール人 is supposed to mean Chinese Singaporean. I was told of this term by a Chinese Singaporean who can speak Japanese.
According to the dictionary I use, 中華 means Chinese food, China. However all examples of Japanese terms for Chinese food given in the dictionary have 中華 refer to China, not Chinese food.
I wish more native Japanese people could comment on having 系 to refer to lineage, ancestry and family line. Many Thanks!