Incremental refresh with polling expression

Go with the timestamp that has the most even distribution (likely the created date).  Create a large enough "hot"  window to cover most of the jitter (modifications happening soon after creation).  For example make your "hot" partitions the last three months instead of the last month.  Then use the Modified date to catch any entries that fall outside the "hot"  window and manually refresh their partitions if needed.  Plan on doing a full refresh (or a sequential manual refresh of all partitions)  every now and then.

No, based on what you've said the problem is with the performance of the SQL queries themselves and nothing to do with Power BI. You need to get a DBA or someone familiar with SQL performance tuning to help you here.