Looking at your original code, to include just the fields elimiating the field_groups option should do what you want
<?php
acf_form(array(
'post_id' => 'new_post',
'fields' => array('field_55fbd2ec6359f', 'field_560e37f2d8763'),
'post_title' => true,
'post_content' => true,
'new_post' => array(
'post_type' => 'my_custom_post_type_name',
'post_status' => 'publish'
)
));
?>
