It seems to me like the best crit-fishing Paladin build is Half-Elf Oath of Vengeance Paladin (6+X) | Hexblade (1+Y), with the Elven Accuracy feat, and the option of mixing in 3+ Sorcerer levels for better spell slot progression and Quickened booming blade if desired. Hexblade gives you a lot...
I think it's worth noting that the Tiger totem level 14 ability plays very nicely with polearms: just charge in, make a bonus action attack, and move back without provoking OA's to repeat on your next turn. If you have polearm master, they will likely draw a reaction attack when they pursue you.