I owned the Line 3SE for awhile, and liked it but didn't find that it did much more for me than my SS pre at the time. I also thought the bass was just a bit loose and lacking in detail. If you can put up with no remote and a clunky 23 step volume control, you might look at either of these preamps. They sound great with solid tight bass, exceptional soundstaging and dimensionality, and grainless high frequencies. These can easily drive any length balanced output cable. Linestage tubes are 12AU7 and 6SN7.
http://cls.audiogon.com/cgi-bin/cls.pl?preatube&1170283497
http://cls.audiogon.com/cgi-bin/cls.pl?preatube&1170169406
The BAT and ARC models you listed are both supposed to sound great also. You would do best to try them in your own system, if possible, so you know if they really sound better to you than your Line 3SE.
http://cls.audiogon.com/cgi-bin/cls.pl?preatube&1170283497
http://cls.audiogon.com/cgi-bin/cls.pl?preatube&1170169406
The BAT and ARC models you listed are both supposed to sound great also. You would do best to try them in your own system, if possible, so you know if they really sound better to you than your Line 3SE.