Instead of using
IMPORTRANGE use Google Apps Script
According to Change a spreadsheet's locale, time zone, recalculation, and language the recalculation interval for
IMPORTRANGE is 30 mins. If shorter recalculation interval is needed then somehow the formula parameters should be changed.
Unfortunately, in the new Google Sheets is not possible to use
RANDBETWEEN functions, so the alternative is to use a Google Apps Script.
Explanation about the use of non-deterministic functions
In the thread provided in the comment by Jacob Jan Tuinstra it's mentioned the use of an extra URL parameter that it's updated at certain intervals. That thread is from 2011.
The core idea was to add to the URL something like
"&workaround="&NOW() and set the recalculation setting to
on change and every minute but this could be too frequent as the import task could take more than one minute, so instead of
NOW() you should round it to a good enough interval, let's say 10 minutes, then instead of
Let name this formulas
The cell formula containing
IMPORTRANGE will look like this
Unfortunately the above formula returns the following error
This function is not allowed to reference a cell with NOW(),
RAND(), or RANDBETWEEN()
The same happens with the other import functions (