335 fields in one table? !!!! That's a very extreme number of fields for one table. That may be necessary, but any time the count starts to exceed 100, I suggest re-examining your design to see if it is possible to reduce the number of fields in one table--possibly by putting some in a related table. That isn't always possible of course....
Try this trick:
Create a blank layout to use as the new layout. Add layout parts and change their sizes as needed to match those of the layout you intend to duplicate. (You can click a part's label and then see its height in the Inspector's Position tab. You can click the units to cycle units until you see that dimension in pixels (fileMaker 11 and older ) or Points (Filemaker 12 and newer).
Go to the layout you want to duplicate, enter layout mode and copy all the objects on your layout. If this is FileMaker 12, use the inspector to group the objects into a single group before you copy them. In any version, then use the Inspector's position tab to note the top and left values in pixels/points while the objects are selected.
Now go to Manage | Database | Relationships. Find the Tutorial: What are Table Occurrences? box specified in Layout Setup | Show Records From for the original layout. Double click it and temporarily change it's name. Find the Table Occurrence for the new layout and edit its name to be exactly that of the first Table Occurrence (to what it was before you changed it). Click Ok to dismiss Manage | Database.
Now go to the new Layout and Paste your layout objects from the clipboard. Use the top and left boxes in the Inspector's Position tab to adjust the position of the pasted objects to exactly match that of the original layout. If this is FileMaker 12, you should then ungroup your pasted group of objects. Save your layout changes (Enter browse mode) and then you may go back to Manage | Database to change your table occurrence names back to their original values if you wish.