Deaf and Hard-of-Hearing (DHH) users face accessibility challenges during in-person and remote meetings. While emerging use of applications incorporating automatic speech recognition (ASR) is promising, more user-interface and user-experience research is needed. While co-design methods could elucidate designs for such applications, COVID-19 has interrupted in-person research. This study describes a novel methodology for conducting online co-design workshops with 18 DHH and hearing participant pairs to investigate ASR-supported mobile and videoconferencing technologies along two design dimensions: Correcting errors in ASR output and implementing notification systems for influencing speaker behaviors. Our methodological findings include an analysis of communication modalities and strategies participants used, use of an online collaborative whiteboarding tool, and how participants reconciled differences in ideas. Finally, we present guidelines for researchers interested in online DHH co-design methodologies, enabling greater geographically diversity among study participants even beyond the current pandemic.