Magento 2 – How to Get EAV Attribute Value from Model Class

It's possible.
When I create an EAV entity I make the entity model extend Mage_Catalog_Model_Abstract, the resource model extends Mage_Catalog_Model_Resource_Abstract, and the resource collection model extends Mage_Catalog_Model_Resource_Collection_Abstract.
This way the entity behaves in a similar was to the product or category entity.

You can give this module creator a try. It's not yet in a final stage but it should work for simple modules. It has support for creating EAV entities.

If you got orphan attribute values it means that there is something wrong with your database.
For example the table catalog_category_int has a constraint on the attribute_id column.

CONSTRAINT `FK_CAT_CTGR_ENTT_INT_ATTR_ID_EAV_ATTR_ATTR_ID` FOREIGN KEY (`attribute_id`) REFERENCES `eav_attribute` (`attribute_id`) ON DELETE CASCADE ON UPDATE CASCADE,

This means that if the attribute is deleted, all the values for the attribute from the table catalog_category_int will be deleted.
It's the same for the rest of the tables (catalog_category_*).

From experience I saw that usually constraints are lost during a migration process. You export the database but without the constraints. If this is the case then remember in the future to use System->Tools->Backupto create database dumps for migration.

[EDIT]
Here is the code I've used. I've created a simple extension that adds an attribute to the category entity, I edited a category and filled in a value for that attribute, then deleted the attribute through an upgrade script.
Here are the extension files:

app/etc/module/Easylife_Attr.xml - declaration file

<?xml version="1.0"?>
<config>
    <modules>
        <Easylife_Attr>
            <codePool>local</codePool>
            <active>true</active>
            <depends>
                <Mage_Catalog />
            </depends>
        </Easylife_Attr>
    </modules>
</config>

app/code/local/Easylife/Attr/etc/config.xml - the configuration file

<?xml version="1.0"?>
<config>
    <modules>
        <Easylife_Attr>
            <version>0.0.1</version>
        </Easylife_Attr>
    </modules>
    <global>
        <resources>
            <easylife_attr_setup>
                <setup>
                    <module>Easylife_Attr</module>
                    <class>Mage_Catalog_Model_Resource_Setup</class>
                </setup>
            </easylife_attr_setup>
        </resources>
    </global>
</config>

app/code/local/Easylife/Attr/sql/easylife_attr_setup/install-0.0.1.php - the install script

<?php

$this->addAttribute('catalog_category', 'dummy', array(
    'group'         => 'General',
    'input'         => 'textarea',
    'type'          => 'text', //can be any type
    'label'         => 'Custom attribute',
    'backend'       => '',
    'visible'       => true,
    'required'      => false,
    'visible_on_front' => true,
    'global'        => Mage_Catalog_Model_Resource_Eav_Attribute::SCOPE_GLOBAL
));

Now add a value for this dummy attribute for a category.
You should see it in the table catalog_category_entity_text.

After that create an upgrade script to remove the attribute. app/code/local/Easylife/Attr/sql/easylife_attr_setup/upgrade-0.0.1-0.0.2.php

<?php
$this->removeAttribute('catalog_category', 'dummy');

and change in config.xml the version from 0.0.1 to 0.0.2.

Refresh any page and look in the same table catalog_category_entity_text. The value that was added for the dummy attribute is gone. (at least for me).