Yes, I'm leaning most towards proposition 2 now: Remove timers from both exploders in singleplayer, keep everything as-is in multiplayer. The skills need to become more different in the panel.
Proposition 3 is an alternative, removing the L1 bomber timer, and deprecating its usage in multiplayer.
By now, there are too many levels dependent on the non-flinging physics of the L1 bomber. From multiplayer design, the L1 bomber is a barnacle that has attached to the ship and can't be scrubbed off easily by now. From a singleplayer level designer's viewpoint, however, the L1 bomber is more valuable than the L2 exploder. Thanks to the various level authors for sharing their ideas here.
Nepster is right in how arguing against the L1 bomber provides arguments against the L2 exploder instead. The L2 bomber will stay in at all costs for now. This is an important attacking skill in multiplayer.
Design history: The L1 bomber came in 2006, when I was aiming at a Lemmings 1 clone, as a learning project for C++. Everything should be close to L1, but with bugfixed physics if possible. I did not care much about contemporary game design back then.
The multiplayer mode came in 2008, and the L2 exploder had to come because blockers on steel turned out unremovable by the opponents. Level exits had to have lots of steel around them, and the L1-included levels had lots of steel in general. The batter was a much later addition in 2011.
-- Simon