Squire/Countess-->Squire (has much better damage output, and the Countess' Joust ability can send her off walls to her death)
Incorrect. The Squire does not have better damage output, the Countess does, having speed and strength 20% better, but worse health and casting ability. They are fairly evened out depending on what you want to do with them.
Apprentice/Adept-->Adept (neither is much good at DPS (it's better to focus on towers as these classes) and their stats are very similar, but the Adept moves faster and can instantly upgrade/repair Defenses, making her more useful in combat.
Moving fast isn't everything, and instant upgrade/repair is utterly useless as it's basically a watered down version of the Apprentice's Overcharge, which rapidly speeds all casting, not just upgrading and repairing. So it appears you completely overlooked overcharge. Not to mention that Mana Bomb has far more use than Purity Bomb. In fact, the only thing the Adept has got going for it is that it walks faster than the Apprentice.
And to be fair, with the exception of the Adept the genderswapped classes don't really outclass the originals as much as they are better suited to different builds.
You will also want a Barbarian on any map that requires a a lot of DPS done. (e.g. Monsterfest maps)
A Series EV is also pretty much necessary on any nightmare map due to the Tower Buff Beams.
A Jester can be your worst enemy or your greatest ally, for they have one of the most powerful hero abilities in the game: the wheel of fortune, which can buff enemies, slow enemies, kill off a percentage of enemies, debuff enemies, damage all enemies, downgrade towers, upgrade towers, heal allies, and a few more. They can also wield any weapon, and the presents that are their towers can spawn any tower, sometimes for less defense units than they would be ordinarily, to an ogre.
The most successful strategy is to use all towers possible. In the nightmare difficulty, it is very difficult to get by without using a combination of the Monk's Auras, the Huntress' traps, either the Squire's or the Apprentice's towers (preferably the Squire's because enemies can be immune to elements), the EV's beams and the Summoner's Minions.