Castbound

If luck is what you are after, Castbound has an enviable number: 390 Luck, 3rd of 184 obtainable rods. It is a quest reward at Underground Music Venue, it carries a passive, and the wiki flags it as a level-required rod, so it is not something you can walk into on day one.

The tradeoff is that the other stats are middle of the road. Control of 0.14 is 70th of 185 and Resilience of 32 is 50th of 184. No Lure Speed is listed, so we cannot say how fast bites arrive, and no weight cap is given either. In practice, the rod is about rarity of catch, not about comfort or speed.

The wiki's description is a sword forged as the end of a long road, which fits a late-game reward. If you are working toward it, plan around the level requirement and the quest rather than a shop, because it is not listed with a price. Players who already have a luck rod will see the biggest jump here only if their current Luck is well under 390. The same venue also lists Cinderstring, Axe of Rhoads, Wingkeeper, Acidgrinder and Eardrum for comparison.