I'd support the first alternative with the reasoning that file positions for ASCII files should be treated as opaque 'cookies', that is, you can get the file position and set it to get back to a point where you were before, but you should not do arithmetic with them.
[other less pleasurable options deleted]
You have to do something like this, anyway, to support multi-byte characters, so you may as well do lineEndConvention this way, as well.
-- Mike
GO unicode!