This paper presents methods for building speech recognizers tailored for Japanese speaking assessment tasks. Specifically, we build a speech recognizer that outputs phonemic labels with accent markers. Although Japanese is resource-rich, there is only a small amount of data for training models to produce accurate phonemic transcriptions that include accent marks. We propose two methods to mitigate data sparsity. First, a multitask training scheme introduces auxiliary loss functions to estimate orthographic text labels and pitch patterns of the input signal, so that utterances with only orthographic annotations can be leveraged in training. The second fuses two estimators, one over phonetic alphabet strings, and the other over text token sequences. To combine these estimates we develop an algorithm based on the finite-state transducer framework. Our results indicate that the use of multitask learning and fusion is effective for building an accurate phonemic recognizer. We show that this approach is advantageous compared to the use of generic multilingual recognizers. The relative advantages of the proposed methods were also compared. Our proposed methods reduced the average of mora-label error rates from 12.3% to 7.1% over the CSJ core evaluation sets.