They could just bring in extra settlers from Japan like what China did, and after lots and lots of fighting, marginalise the Taiwanese Aboriginals in the end. If Japan's being more proactive, that means they inevitably have a stronger government and thus more centralisation than they did historically, so they could move people around like this. And if I recall, the Japanese islands were always toward the upper end of their carrying capacity.
That could also be a reason to secure Sakhalin and Hokkaido far ahead of OTL. The Japanese could definitely settle the islands on their own and displace the natives if someone pushed settlement there and encouraged the Japanese to spread out over the 5 islands of the Japanese archipelago. Not to mention, once Japan realises that Russia is establishing interests in the Far East (disregarding butterflies), Japan will likely want to counter that, meaning they'd probably assert control over Kamchatka with forts and such.