HAVING all but won the race to be Japan's next prime minister after decades of preparing for it, Kiichi Miyazawa faces a more daunting test over his ability to lead.Even though he is perhaps the most experienced and international of Japanese politicians, Mr. Miyazawa may have had to compromise his policies and authority - as have recent prime ministers - in order to win key support from leaders of the most powerful faction of the ruling Liberal Democratic Party (LDP). But the smiling and sharp-tongued Miyazawa has not said what he promised the faction headed by former Prime Minister Noboru Takeshita in order to line up enough party votes to win an Oct. 27 vote for party president. That vote will automatically make him prime minister. As a result, the Miyazawa known by many foreign leaders over the decades may not hold the same views as Prime Minister Miyazawa. "We hope that the Miyazawa government will show a strong political stance of its own, so that it is not called a puppet of the Takeshita faction," stated Japan's largest newspaper, the Yomiuri. Ironically, Miyazawa campaigned for the post by criticizing Prime Minister Toshiki Kaifu as an ineffectual leader beholden to the Takeshita faction. Miyazawa may be less malleable than Kaifu, but he holds strong and independent views on important issues that could put him at odds with the LDP mainstream. Such issues include whether to import rice, revise the Constitution to allow overseas military deployment, and set up a single-seat electoral system. "Miyazawa will never bow to the Takeshita faction," says political analyst Minoru Morita, who knows Miyazawa well. But before the Takeshita faction backed him on Oct. 11, the elder Miyazawa was forced to meet one of the faction's younger power-brokers, Ichiro Ozawa, who quizzed him on his policies. The next day, Miyazawa said that the Takeshita faction would be able to get key Cabinet and top party posts. The comment revealed a back-room deal and Miyazawa was forced to apologize. It also raised speculation among political observers that Miyazawa may only last as prime minister until the party makes it through an election for the upper house sometime next year. The LDP lost control of the upper chamber in 1989. Leaders of two other factions, Michio Watanabe and Hiroshi Mitsuzuka, vowed to stay in the party election despite Miyazawa having lined up support from three of the LDP's five factions. Mr. Watanabe asked LDP members to vote their political conscience rather than their factional loyalty. But such independent voting would be a rarity in Japan, leaving political analysts noting that the Oct. 27 election will be democratic in form only, with Miyazawa already selected by LDP power-holders.