The easiest way is to use the "assignMultiple" action module to assign any custom forms you need, as this module will accept a list, and then update your custom properties as a second call.
They do not need system administrator access. If all they are doing is polling for data, then they just need a basic user account that would be able to see that data normally.
Instead of doing it in a filter, you could just add it as a parameter to your query, to the effect of lastUpdateDate = {today -2}lastUpdateDate_Mod = gt
It is possible to create a webhook with OR filters doing it with the raw API, but Fusion's webhook creator hasn't been updated for that new functionality, as far as I know.