Trying out the new 1.6.1 release (v 8.9.0.751) (Edit: while writing this, a new version was put up, I'll check that one), but every time Minecraft is restarted, I connect to servers as a new player.
It was a fresh install, as per the instructions I found here: http://www.minecraftforum.net/topic/1873892-updating-installing-mods-in-161/
Aside from this issue, it seemed to load just fine--the mods were listed on the Minecraft game window.
In the log, I noticed this in particular:
2013-07-02 01:52:45 [iNFO] [sTDOUT] Completely ignored arguments: [MY-USERNAME, token:79f9baeddeac4090bc909961dc7dcd6c:1f18210167cb455d927549bf24e86a08]
Here is the full ForgeModLoader-client-0.log:
http://pastebin.com/raw.php?i=ceJEWYeB
and here is the new launcher's development console:
http://pastebin.com/raw.php?i=q0F3KuUy