I would like to add here, in Power BI Desktop, query Editor, you have the option to disable the load query so the query is not refreshed. When you disable the load, you will not slow down the performance of the servers and will improve the performance of Power BI Desktop report.
If the SQL refreshes are timing out, you are probably correct that you are pulling too much data at once, but, doing all of the joins in the SQL may also slow it down more.
I am a SQL person first and a Power BI person second, so I look at things a little differently from most people on this forum.
1) I like bringing in all of the tables individually and using the relationships in Power BI rather than "flattening" my data source by doing all of the joins when pulling in the data. This gives me more power for creating my formulas, etc inside of Power BI.
2) I would prefer to bring in one table at a time with a query for each tables (some denormalization where it makes sense by doing the joins) if I need to remove a lot of columns or some of the rows. This way, if the SQL database is optimized properly, it will take much less time to refresh. Rather than pulling in all of the data and then removing a bunch, we only pull what we need.
On your comment from page 3 that I responded to earlier. I realized you missed where the other user was putting in the M code. It is after the import happens, by clicking Advanced Editor on the Home tab of the Power Query Editor.
For books, to understand the concept of normalization that I mentioned earleir in this comment, I recommend any of the edtitions of Jan Harrington's Relational Database Design Clearly Explained. I like the 1st edition best if you can find it in a used book store.
For writing T-SQL (MIcrosoft's flavor of the SQL language - stands for Transact-SQL) there are a huge number of books to choose from. If you are going to be doing a lot of query writing and don't have an IT team to create VIEWS that already have what you need in them, I recommend taking a 3 day course. If you like learning on your own, one of the most popular books are the ones by Itzik Ben-Gan. Either T-SQL Querying or SQL Fundamentals.