As long as you're implementing your own platform independent menus, then why don't you implement pie menus, like I implemented for the HyperTIES hypermedia browser at the University of Maryland Human Computer Interaction Lab in the 1980's? (For another more recent example, see the pie menus in The Sims from 2000.)

Demo of The Sims Pie Menus:
https://www.youtube.com/watch?v=-exdu4ETscs

Designing to Facilitate Browsing: A Look Back at the Hyperties Workstation Browser

By Ben Shneiderman, Catherine Plaisant, Rodrigo Botafogo, Don Hopkins, William Weiland.

Human-Computer Interaction Laboratory,
A.V. Williams Bldg., University of Maryland,
College Park MD 20742, U.S.A.

http://www.donhopkins.com/drupal/node/102

http://drum.lib.umd.edu/bitstream/handle/1903/362/CS-TR-2433...

Pie menus to permit low cognitive load actions:

To avoid distraction of common operations such as page turning or window selection, pie menus were used to provide gestural input. This rapid technique avoids the annoyance of moving the mouse or the cursor to stationary menu items at the top or bottom of the screen.

3. PIE MENUS TO PERMIT LOW COGNITIVE LOAD ACTION

The Hyperties browser uses pie menus as accelerators, to make commonly used commands quickly and easily available. A pie menu is a type of pop up menu whose selections are laid out in a circle around the menu center (18). The menu pops up centered on the cursor, so that each selection is adjacent to the cursor but in a different direction (Figure 1 and 6). A selection is made by moving the cursor in the direction of the desired selection, and clicking. Experienced pie menu users can make selections from familiar menus quickly and reliably without even having to look at the menu, because the menu selection depends on the direction between the two mouse clicks that invoke and select from the menu. The distance of cursor motion does not effect the selection, but the further away from the center the cursor is, the more precise the control of the selection is.

The browser has a control panel at the bottom of the screen, with buttons showing the names of available commands, to turn the page, return to the previous article, show the index, etc. When users are browsing a document by pointing and clicking on highlighted text links in the main contents window, they move the cursor down to the bottom of the screen to press buttons in the control panel, and back up to continue browsing. The permanent display of those controls is important for the novice and occasional users. On the other hand, pop up menus reduce the distraction of moving the cursor by making these commands available wherever the cursor currently is. This reduces perceptual and motor load. Pie menus are arranged with their items in easy to remember directions. For example the BACK page turning commands are to the left (and the NEXT page is to the right) (Figure 6). This arrangement facilitates gestural input and encourages development of muscle memory. Experienced users can make gestural selections from these menus so comfortably and rapidly that it is often unnecessary to display the menu. This is called "mouse ahead display suppression", and its point is to reduce the perceptual distraction.