I got it working. asanaTasksApiInstance.updateTask is backwards from asanaTaskTemplatesApiInstance.instantiateTask.
This works:
const updateBody = {
"data": {
"custom_fields": {
"1171036591936079": req.body.customerNameGid
}
}
};
const updateResult = await asanaTasksApiInstance.updateTask(updateBody, newTaskGid);