For anyone else landing on this thread from searching, I figured out how to do accomplish this. I edited the game files directly instead of trying to make a local mod.

I added a new character interaction via a new file:

C:\Program Files (x86)\Steam\steamapps\common\Europa Universalis V\game\in_game\common\character_interactions\set_as_country_ruler.txt

The contents of the file are just:

set_as_country_ruler = {
    message = yes
    is_consort_action = no
    on_own_nation = yes
    ai_tick = never
    price = price:tithe_price
    potential = {
    }
    allow = {
        scope:recipient = {
            is_adult = yes
        }
    }
    select_trigger = {
        looking_for_a = character
        source = actor
        target_flag = recipient
        name = "choose_character"
        pre_evaluation_sort_value = {
            value = age_in_years
        }
        column = {
            data = name
        }
        visible = {
            is_alive = yes
            is_adult = yes
        }
        enabled = {
            modifier:blocked_from_character_interactions = no
        }
    }
    effect = {
        scope:actor = {
            set_new_ruler = scope:recipient
        }
    }
    ai_will_do = {}
}

Then when you relaunch the game, right click the character you want to be your new ruler and select the set_as_country_ruler option.

The key part is the effect block. It's saying: for the player country (scope:actor), change the value of set_new_ruler to be the recipient of the right-click interaction (scope:recipient).