A third option that I'd like to see (maybe in conjunction with your first suggestion) is that all LB's only consume one bar.

Basically, if you have 3 full bars, using an LB would trigger your LB3, but only one bar would be consumed, making an LB2 still available.

Not quite as OP as 'everyone has their own LB meter' but it would at least allow for you to have multiple LB's in a dungeon.
And if you blew a LB1 as a Tank/DPS earlier, while you might not have an LB3 saved, your healer could at least get some support from an LB1 or 2.

This should at least get some use of LB 1 and 2, considering that these aren't actually a dps gain at all at higher levels, and I think LB2 may actually be a dps loss considering the animation lock. So with a little buffing as well, that would be useful.