There's at least one shortcut that uses control, option, shift, and command, ⌃⌥⇧⌘., which saves a sysdiagnose report to /var/tmp/.

The reason why key combinations like ⌥← don't work with Unicode Hex Input is probably because they aren't assigned to control characters. I got ⌥← to work after adding this to keymap 3 in the Unicode Hex Input.keylayout that comes with Ukelele:

    <key code="123" output="&#x001c;"/>

You could also use DefaultKeyBinding.dict for inserting Greek characters, but it wouldn't work in Xcode or shell views. (See http://www.hcs.harvard.edu/~jrus/site/KeyBindings/Greek%20Bi...) Another option would be to add keymaps to a keylayout file:

    <keyMapSelect mapIndex="8">
        <modifier keys="caps"/>
    </keyMapSelect>
    <keyMapSelect mapIndex="9">
        <modifier keys="caps anyShift"/>
    </keyMapSelect>
    
    ...
     
    <keyMap index="8">
        <key code="0" output="α"/>
        <key code="1" output="σ"/>

To assign another key to a holdable caps lock, check "Pass-Through CapsLock LED status" and add something like this to private.xml:

    <autogen>
    --KeyToKey--
    KeyCode::N,
    Option::KEYTOKEY_BEFORE_KEYDOWN,
    KeyCode::CAPSLOCK,
    Option::KEYTOKEY_AFTER_KEYUP,
    KeyCode::CAPSLOCK
    </autogen>

I thought something like this might also work:

    <autogen>
    --KeyToKey--
    KeyCode::A,
    ModifierFlag::OPTION_R,
    KeyCode::A,
    Option::KEYTOKEY_BEFORE_KEYDOWN,
    KeyCode::VK_CHANGE_INPUTMODE_RUSSIAN,
    KeyCode::VK_WAIT_10MS,
    Option::KEYTOKEY_AFTER_KEYUP,
    KeyCode::VK_WAIT_10MS,
    KeyCode::VK_CHANGE_INPUTMODE_FINNISH
    </autogen>

Unicode Hex Input or Greek is not included in inputsourcedef.xml though.