Which melee weapons have the Two-Handed and Reach property, but lack Heavy and Special?

For my Kensei monk I’m exploring potential additional kensei weapons.

Kensei Weapons. Choose two types of weapons to be your kensei weapons: one melee weapon and one ranged weapon. Each of these weapons can be any simple or martial weapon that lacks the heavy and special properties. The longbow is also a valid choice. You gain proficiency with these weapons if you don’t already have it. Weapons of the chosen types are monk weapons for you. Many of this tradition’s features work only with your kensei weapons. When you reach 6th, 11th, and 17th level in this class, you can choose another type of weapon – either melee or ranged – to be a kensei weapon for you, following the criteria above.

At level 3 I picked the longsword and longbow. At level 6 I’d like to pick a two-handed non-heavy non-special melee weapon, preferably with reach. Conceptually, a polearm would be sweet. Mechanically, a damage die of 1d8 or higher would be awesome.

Going through the list of equipment a couple times now, I seem to have only three options that come close:

  • a greatclub has two-handed but lacks reach.
  • a whip has reach but lacks two-handed.
  • a lance has reach and “kind of two-handed”, but also has the special property (so can’t be a kensei weapon unfortunately).

Are there actually such weapons, by RAW, that fulfill my wishes? In other words, is my source for equipment up-to-date with all the released books, including the playtest material of Unearthed Arcana?

In case it matters: I like the idea of wielding a two-handed reach weapon as an unarmored old man, because I think it’s cool. It’s inspired by dextrous martial artists IRL that wield relatively light polearms.