I don't have any experience in this but if you really need to load big files I suggest you do some kind of lazy loading with JTextPane/JEditorPane.
Define a limit that JTextPane/JEditorPane can handle well (like 500KB or 1MB). You'll only need to load a chunk of the file into the control with this size.
Start by loading the 1st partition of the file.
Then you need to interact with the scroll container and see if it has reached the end/beginning of the current chunk of the file. If so, show a nice waiting cursor and load the previous/next chunk to memory and into the text control.
The loading chunk is calculated from your current cursor position in the file (offset).
loading chunk = offset - limit/2 to offset + limit/2
The text on the JTextPane/JEditorPane must not change when loading chunks or else the user feels like is in another position of the file.
This is not a trivial solution but if you don't find any other 3rd party control to do this I would go this way.