Early diagnosis of Alzheimer's disease (AD) is crucial in facilitating preventive care to delay further progression. This paper presents the development of a state-of-the-art Conformer based speech recognition system built on the DementiaBank Pitt corpus for automatic AD detection. The baseline Conformer system trained with speed perturbation and SpecAugment based data augmentation is significantly improved by incorporating a set of purposefully designed modeling features, including neural architecture search based auto-configuration of domain-specific Conformer hyper-parameters in addition to parameter fine-tuning; fine-grained elderly speaker adaptation using learning hidden unit contributions (LHUC); and two-pass cross-system rescoring based combination with hybrid TDNN systems. An overall word error rate (WER) reduction of 13.6% absolute (34.8% relative) was obtained on the evaluation data of 48 elderly speakers. Using the final systems' recognition outputs to extract textual features, the best-published speech recognition based AD detection accuracy of 91.7% was obtained.