Ok,
This is a database hack.
If you look carefully the menu table structure, you can see 'level', 'lft' and 'rgt' fields.
When you see theses names, you are sure you cannot HACK the table easily.
Left, Right and Level are system fields for hierarchical system (Nested system)
If you add an entry in this table, you destroy everything. Did you tried ?
In future version of Cook, the Nested table will be handled, and maybe such hacks possible.
BUT BE VERY CARFULL !!
I think you can realize your component using derectly the MVC of the menu component.
Add some includes to load the model, and the table files related to com_menu.
Try to understand how com_menu works, and copy the essential actions, functions... in your component.
The most important is to use com_menu data access functions (should be in model, and table files. I didn't have a look yet)
A review of your experience will be very appreciated.