To have a more lasting Hindu influence on Japan is not impossible. Deities such as Fujin, Raijin and perhaps even Inari Okami combine aspects of the Rigvedic Deities, Vayu, Indra and Uma Haimavati respectively. However these were fully Buddhist interpretations of these deities, archaic remnants from the time of the Pali Canon, so they can be discarded as they really didn't represent the mass form of Hindu deities in Southeast Asia or on the Subcontinent.
The best way would be for the Champa fleets of Indrapura to actually remain premier rather than those of Panduranga or Vijaya. Majapahit traders and Shaivite saints had already spread the first inklings of Hinduism to the Phillipines by the late 10th century and it was spreading fast in Luzon as far as I know. If the Indrapura fleets which used to regularly visit Taiwan and Luzon continue to do so it might not be long before the faith starts island hopping up the Ryukyus.
Concepts such as Harihara and the cult of the Devaraja would jive very well with the Heian period emperors and if the faith manages to entrench itself it would most likely syncretise with Shinto and Buddhist practices to re-establish itself in a new method. And since Buddhism had already entered Japan via China the Buddhist thought from Srivijaya and the Khmer empire that enters Japan might provide a competing school of thought for it.