1-2 levels can't be right. My bar has never NOT been full since 3.0 came out. I hit omni-50 well before 3.0 came out, and I made it from 50 to 60 on 15 classes so far and my bar has still never not been full. Even if it doesn't count exp from quests, a lot of that exp was from synthing, quicksynthing, gathering, and fishing, all of which definitely do get the rested bonus...
EDIT: Aha! Research! The rested cap IS 1.5 levels. However, it's not "until you've gained 1.5 levels" it's "until you've gained bonus exp equal to 1.5 levels." This means that, for second classes (meaning, with the +50% armory bonus for not being your highest), you can gain 6 levels from pure grinding before you lose the rested exp bonus (1.5/(0.5/(1+0.5+0.5)) = 6). Without the armory bonus, you would lose it after "only" 4.5 levels of pure grinding (1.5/(0.5/(1+0.5)) = 4.5). Since you aren't doing pure grinding, and since you are logging out in towns and not playing 24/7, you are still accumulating rested exp at some rate, causing that to stretch beyond the 6/4.5 level limit. And, since you're gaining exp that isn't boosted by the bonus (ie: from quests), and that exp is likely at least 3x what you're getting from grinding sources, you can easily get a good 20 levels before losing your bonus.
Oh, and if your FC runs the 10% exp buff for your type of leveling (Heat of Battle II, Earth and Water II, Helping Hand II), that becomes even more: (1.5/(0.5/(1+0.5+0.5+0.1))) = 6.3 levels, or (1.5/(0.5/(1+0.5+0.1))) = 4.8 levels.
My meter never ran out because 1.5 levels is a lot when you're going 50->60. Since I wasn't playing 24/7, I must have gained enough to stretch that bonus out enough to gain the 150 levels I gained without losing my bonus. BUT! If you do PURE grinding, you'll run out after 6 levels are gained (4.5 levels if it's your highest class).
Source: https://www.reddit.com/r/ffxiv/comme..._is_15_levels/