[Fyron]

If I added more troop transports, but no other ships with cargo capacity, that should allow me to capture one planet/moon per TT, right?

Right. Even having ships with other cargo capacity will still let you capture one planet/moon per TT. The problem comes in loading cargo to capture in more than one sector per turn. You have to be more careful to load cargo from every planet in the sector, or you will leave troops behind.