How about a mod/DLC that allows you to have different origin after completing the original version of the game? Where you could be Synth, Ghoul, heck even a child character, to allow greater customization/replayability?

Option one: your character died while in Cryo, and your character's memory was downloaded into a Synth body.

You discover that you aren't who you thought you are, and have deal with those who fear/distrust Synths, let alone how the different factions feel about it. That would give Father a whole different meaning. A trip to Memory Den may reveal the shocker to the player....

Option two: the cryopod was badly malfunctioning and cause it to be irradiated, turning the player into a Ghoul, rather than going into cryogenic suspension. Being a Ghoul, of course, has it own pros and cons in Fallout, such as how certain settlements might feel about Ghouls. Also, some perks can have some modifications, such as starting out with an enhanced version of Rad Resistant and Ghoulish with the offset that most people have a negative outlook to 'zombies', feral or otherwise. Some of the charisma perks could be modified to represent your character working to overcome as much negative bias as possible.

Option three: your character died after having Shaun, but you were successfully cloned and placed in an accelerated maturation chamber. The government-funded facility (maybe a subsidiary of Vault-Tech) had their funding revoked just before the War, releasing your character before he/she was scheduled to be ready to pick up his/her normal life before whatever killed the character in the first place.