FactoryGirl belongs_to with Seeded association

I have a UserType object that ideally is seeded in the DB and remains static:

{id: 1, name: 'Individual'}, {id: 2, name: 'Group'}, {id: 3, name: 'Admin'}

class UserType < ActiveRecord::Base
  attr_accessible :name
  has_many :users
end
class User < ActiveRecord::Base
  attr_accessible :email, :first_name
  belongs_to :user_type
end

In testing, I simply want to create an admin user that has its user_type_id field set to 3 when created, and for the UserType.all to have those three items. I've tried a number of things, but here's where I'm at:

FactoryGirl.define do
  factory :user_type do
    id 1
    name "Individual"
    description "An individual account (B2C)"

    trait :group do
      after(:create) do |user_type|
        id 2
        name "Group Leader"
        description "A leader/manager of group visits"
      end
    end
    trait :admin do
      after(:create) do |user_type|
        id 3
        name "Administrative"
        description = "A user of the Enrollment Generator"
      end
    end
  end
end

FactoryGirl.define do
  factory :user do
    first_name 'TestUser'
    email { Faker::Internet.email }

    user_type    

    trait :admin do
      after(:create) do |user|
        admin_user_type = UserType.where(id: 3).first
        admin_user_type = create(:user_type, :admin) unless admin_user_type
        user_type admin_user_type                    
      end
    end

  end

And my test in spec/features/sessions/admin_sign_in_spec.rb:

feature "Admin signing in" do
  background do
    @institution = create(:institution_with_institutiondomains)
    @admin = create(:user, :admin, email: "admin@#{@institution.subdomain}.com")
  end

  scenario "with correct credentials", focus: true do
    binding.pry 
    @admin.inspect
    page.visit get_host_using_subdomain(@institution.subdomain)
    within("#login-box") { fill_in t('email'), with: @admin.email }
    click_button t('session.admin.sign_in') #the action in signing in here checks that user.user_type_id == 3

    expect(page).to have_content "You're signed in!"
  end
end

I appreciate any guidance.