First, just be aware that "made in Japan" (日本で作られた) does not necessarily imply "Japanese"/"of Japan" (日本の); and vice versa. My <product from American company> could be made in Japan, but I wouldn't consider it a Japanese product. Likewise, I could own set of souvenir Japanese swords, but they could be made in Mexico.
Anyway, on to your question. Barring any nuances I mentioned above, it would be perfectly fine to substitute 日本の and get the same overall meaning. 「日本がもの」 is ungrammatical and doesn't make sense. A better choice might be 「日本製のもの」 if you want to avoid using a verb.
As for whether to use 作る vs. 作られる, I feel like that is mostly a stylistic choice. 日本で作る・作ったもの is more like "a thing they make/made in Japan", although since the topic is omitted in the example, it could imply that it is something that you made in Japan, but then bought in Hawai'i (which then doesn't make sense). So I think the use of 作られた is the safer choice; to emphasize that it was made in Japan, but that we don't care about who the makers are at all.