answering out of turn, everything that lowers the mass and inertia of the level wind makes the greatest difference, because that's a load brake on your cast you can never eliminate, but hope to minimize in slick parts.
The power to move the level wind mechanism during the cast comes off the spool through the idler gear, so the lightened BB idler gear is the place to begin, and BB worm gear goes hand-in-hand.
Bearings through the spool system are gravy, but if you go to the trouble to alter the former, they're parts that need replacing, anyway, and newer bearings with light (or no) oil spin much more freely than older shielded bearings lubed with who knows what.
When you get to slicking up the spool and choose braid, you can make a big difference going to a shallow spool made for braid, because the mass of the line on your spool is always the greatest inertia (slow to start, hard to stop). Also note 12-15-lb braid is about the thinnest to try on a baitcaster, and make sure you check the capacity of that shallow spool.
Of course you can also use this spool with UL mono, equivalent line diameter is 4-lb test, though 6-lb might be a better choice.
Again, the real test is how the reel behaves with light lures. (it's easy for heavy weights to haul away line from a baicaster)
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If you think about the mechanics of a cast, it's ballistics.
The fastest thing that happens is the lure at the end of your swinging rod.
When you release your thumb, everything in the reel uses energy from the cast to accelerate to some line velocity below your initial lure velocity. The lower the system inertia, the higher that peeling line velocity, and the longer your cast.
From that initial acceleration, everything immediately begins slowing down - the ballistic curve.
Since the spool of line has the greatest mass and inertia, by itself, it's the last to slow down.
Everything dragging on the spool is helping to keep it from backlashing, but we still have casting brakes and thumb to slow the spool to match the decreasing lure/line velocity.
Again, it's the maximum velocity achieved by the line coming off the spool that's the biggest factor in cast distance.