Starting
here[
^], I came up with this:
<Style TargetType="{x:Type TabItem}">
<Setter Property="HeaderTemplate">
<Setter.Value>
<DataTemplate>
<ContentPresenter Content="{TemplateBinding Content}" Height="48" />
</DataTemplate>
</Setter.Value>
</Setter>
<Setter Property="Padding" Value="3" />
</Style>
Thank you everyone for brooding over this with me.