It is much, much harder to give players tons of meaningful choices that lets them really feel like they're building their own characters and stories as they play than to have pre-written origin stories. 90% of the time, it feels like the choices a "custom" character has in virtually any game are relatively bland. That's because you have to write to anticipate a million different ways someone might be roleplaying, and it all boils down into meh-dom because if you try to please everyone you please no one.
Basically, you want to non-origins to have access to several tags that none of the origins have. That's a perfectly reasonable request, but a whole lot of work to implement. After all, if you have only one or two non-origin tags, you're not really giving "custom" characters much customization.
Without these tags, I'm not sure what custom characters would have access to that origin characters ought not to. What sort of quest solutions should be available to custom characters that wouldn't be available to origins, without the above tag system solution. Maybe a couple more starting source skills to choose from (maybe three different "dome" effects, where one heals, one deals damage to enemies, and the other is a mix of both.)
GM mode is the place for roleplaying what you want in a satisfying way.