The inline edit form uses some javascript which renders the appropriate editor for the content mimetype. As yours is HTML it will render tinyMCE using the standard set of parameters.
Which are in fact
editorParameters:
{
height: 100,
width: 400,
inline_styles: false,
convert_fonts_to_spans: false,
theme: 'advanced',
theme_advanced_toolbar_location: "top",
theme_advanced_toolbar_align: "left",
theme_advanced_statusbar_location: "bottom",
theme_advanced_path: false,
language: "en",
forced_root_block : false,
force_p_newlines : false,
plugins: "table",
theme_advanced_resizing: true,
theme_advanced_buttons1_add: "fontselect,fontsizeselect",
theme_advanced_buttons2_add: "separator,forecolor",
theme_advanced_buttons3_add_before: "tablecontrols,separator",
theme_advanced_disable: "styleselect",
valid_children : "+body[style]",
extended_valid_elements: "a[href|target|name|style],font[face|size|color|style],span[id|class|align|style],meta
,style[type]" }
There is a form definition for inline edit in share-form-config and you need to ovefride this and force your own editorparameters in share-custom-config.xml
You will use the same default controls but add a <control-param name="editorParameters"> tag and enclose your custom edit options in that