As variant you may create in Excel table like
with 100 days periods staring from TODAY() for the first Date2. Convert dates to Unix Time format (you may google how to do that), query this table. In Power Query create the function which takes data from the site (Period1, Period2 as parameters, but you may add other ones). In PQ add custom column which returns results from the site, remove all other columns, combine this one and return result back to Excel.
100 rows limit most probably added intentionally on server site, java script recognizes who makes the query. Another possible limits could be limit on number of refreshes after first few ones, or time limit between refreshes. Thus such workarounds are not very reliable. Plus limitations could be changed any day and you need to find another workaround. People pushes you to purchase reliable service.