@Davide, if you haven‘t already solved getting the data from custom reports, it is possible to get this data by using the old API and the approach @Ealfardan came up with, see API using excel. Trick is to have checked „Show custom field as column“ so that custom fields appear also in the JSON data in Excel. But of course this entails all the records for each module as it can not be confined to a timeperiod.
out of curiosity, you mentioned it works with trial balance, can I ask how you extract the JSON data for the trial balance at some specific date ?