The problem with not being able to edit the perk trees in the selection menu is...how can the player pick your new perks if there's nothing to click on in the star field?
Sure, you could go to all the work of creating an "Unarmed" perk tree...but without something to click on in the perk selection interface, the player would have to use the console to get them.
Create an invisible NPC that spawns near the player at level-up. Set up all the perk adjustments and stuff through a dialogue. All that would be needed is prompts. It won't be as pretty as the current perk tree menu, but dialogue can branch in the same way that perk trees can. It's just a conceptual work-around, but if perk values can be set through scripting, then the scripts attached to dialogue nodes could allow for it.
After the process is completed, the invisible NPC would delete itself. Or maybe it doesn't have to be invisible. Perhaps it could be spectral, even appear differently depending on which way the perks stack. So if they lean more towards stealth and thievery, you get a rogeu-like ghost in sneak mode standing before you. If your perks favor the warrior, you get an armor-clad ghost. If it favors magic, you get a robed and hooded ghost...
Does this concept have merrit?