I like this idea a lot! The Jacob and Esau one just being a challenge is a little weird to me though. I think maybe they could start with double baby, multidimensional baby, the deserter, and brother bobby, as well as spawn 2 copies of a baby, that take twice as many hearts. Other ones I can think of:
Maggy: Starts with candy heart, and <3, but replaces little chad with double baby. Simple character.
Cain: All active items give you a bunch of coins instead, and you can buy babies at the shop. Also starts with Abel instead of brother bobby.
Judas: Start with no chargers. When you die, you come back, and all babies turn into shadow versions. Shadow versions gain double damage, but cost twice as much and have less health.
B.Baby: Start with the poop, and replace Lil' C.H.A.D. with a new baby called The Relic. This relic takes twice as long, but gives Soul Hearts, which count as double the hearts, but take up the same amount of space in hard mode and such. Meant to be a challenging character.
Eve: Start with a new item called Dead Bird. This makes it so when a baby dies, a bird spawns that harrases and deals damage to the baby's killer. Also, All babies start with lower base damage, but deal 2x the original damage at low health.
Samson: Whenever you lose a charger, all babies gain damage for the chapter. Simple character.
Azazel: Start with a new Lil' Brim baby. All babies have limited range, but can be placed on obstacles. Starts with a unique item called "Hemoptysis", which makes monsters in a 3x3 area take double damage from Lil' Brim.
Lazarus: Revives, but after revival, all heart producers give only 25 hearts each. Simple character.
Eden: Starts with little chad, a random defense baby, a random attacking baby, and a random support baby. Also starts with either 2 random quality 1 items, a random quality 2 item, or a random active item.
Lilith: All babies are blindfolded and have a little incubus floating around. These can attack monsters on the left or right of the baby. Start with lil' chad, demon baby, a new Gello Baby, that shoots normally but whips monsters that get within 3 tiles, and a succubus that boosts the damage of babies in a 5x5 area. Start with box of friends, which summons a second incubus on a baby (and would normally summon one extra incubus on a baby for other character).
The Keeper: All babies start with their shots alternating between triple and quad shot, but much lower health (Like 6 hits from a gaper). You can spend coins to heal your babies.
Apollyon. Starts with the normal deck, as well as a new "Void" Item. All babies start with slightly lower stats, however the void item destroys a baby to give random stat upgrades to babies in a 3x3 area around it. The more the destroyed baby costs, the more stat ups.
The Forgotten: the middle 4 slots are dug up, and cannot have things placed on them. In the middle of these 4 slots is a skull linked to the soul. The skull will attack enemies that get close, and you can use the mouse to move the soul, which shoots like ghost baby.
Bethany: Start with the relic instead of Bob's Brain. Soul hearts charge up the active item. Beth starts with Book of Virtues, which summons a low damage wisp baby. The wisp baby changes depending on what active item is combined with book of virtues.
I think it would be cool if The Lost also started with Lost Soul, allowing you to actually use the 666 hearts to summon it.