There is the setting Recent files list on file menu at Configuration - Toolbars / Menus - Miscellaneous to specify where the recent file list should appear as you already know.
But the recent file list is something where special. This list is automatically managed by the MDI (multi-document interface). An MDI application normally does not need any code line for supporting a recent file list. Maybe there is a special code in UltraEdit to be able to move this list into a submenu of menu File where the MDI normally handles it by default. I'm not a Windows API developer expert, so I don't know it exactly.
However, it is a fact that the recent files list cannot be placed anywhere else on the menu. I have tried it by customizing the menu, but then the recent files list did not work which was no real surprise for me because of the little things I know about the management of the recent files list by the MDI.
So my suggestion is to use File - Recent Files. To open this submenu you have to press Alt+f, then i and last Return or Right Arrow.
But first you need to customize the menu by clicking with right mouse button on it and choosing Customize Menu..., selecting Conversions, pressing the button Edit and deleting the ampersand in Convers&ions. Otherwise after pressing i the wrong submenu is selected and you would have to press i always twice.
I have also a second suggestion which reduces the number of key strokes further. You can customize the menu File and move the submenu Recent Files to top of menu File. The recent files list will work at this position too. Looks like the recent files list must just be present anywhere in the menu File. But with the Recent Files at top of menu File you can activate the submenu now much faster by pressing Alt+f followed by Return or Right Arrow.
Best regards from Austria