It will be difficult, and probably more important, that one question is about stack overflow. Here is some background for you to get started. The class / object you are dealing with above is a block class. Blocks are used for rendering HTML. They, as you have already noted, are stateless.
The block gets its data from the widget instance model object.
Mage::getModel('widget/widget_instance');
Mage_Widget_Model_Widget_Instance
The state of these objects (the data you are trying to change) is in the table widget_instance
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<reference name="content">
<block type="cms/widget_page_link" name="48fc761f38fa9838fcc3a3b498c47f72" template="cms/widget/link/link_block.phtml">
<action method="setData">
<name>anchor_text</name>
<value>asdfasdfsad</value>
</action>
<action method="setData">
<name>title</name>
<value>asdfasdfasdfasd</value>
</action>
<action method="setData">
<name>page_id</name>
<value>2</value>
</action>
</block>
</reference>
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