For overlapping tables, it is best to start with the Autolayout function you have already tried, it should at the very least place the tables in a way they do not overlap each other. If not, make sure you are selecting large enough area in which the tables can fit. Also, try experimenting with the Distance Coefficient settings.
This is a 239 entity model after using Autolayout and tweaking the settings a bit.
As you can see, the tables are no longer overlapping, but navigation in the model might be a bit difficult, due to the sheer number of entities present. You can see that Autolayout has already somewhat divided the model graphically into chunks, you can take this a step further and put each part on a separate Workspace.
You can divide the model into how many Workspaces you want, it is up to you.
To resolve the overlapping lines (well, mostly), you can use the Line Autolayout tool found in Layout Menu. Simply configure it to your liking, for example, you can uncheck Cross Lines and Straight Lines if you prefer lines that do not cross and are not straight.
Just to give an example, this is a part of the original model before and after using Line Autolayout.
Now, you may notice that some lines overlap some tables or that some tables overlap some lines. This can be resolved easily, simply select the lines (or select everything) and from the context menu, choose Line Style | Unhide Line.
Hopefully, this will give you some ideas on how to organize your model. Ultimately, it depends on how you utilize various tools TDM offers.