Same shortcuts across input sources
I tried modifying some non-Latin layouts that came with Ukelele, but couldn't get shortcuts like control+A to work with them. I haven't found a way to get them to work with my custom keyboard layout either, but I'm probably just missing something...

Another option would be to create ~/Library/KeyBindings/ save a property list like this as DefaultKeyBinding.dict:

{
    "^ф" = moveToBeginningOfParagraph:; // ctrl-a on the Russian layout
    "^щ" = (insertNewlineIgnoringFieldEditor:, moveBackward:); // ctrl-o on the Russian layout
    // ...
}


Some of the default control key actions, copied from lri.me/keybindings:

"^p" = moveUp:;
"^n" = moveDown:;
"^b" = moveBackward:;
"^f" = moveForward:;
"^h" = deleteBackward:;
"^d" = deleteForward:;
"^a" = moveToBeginningOfParagraph:;
"^e" = moveToEndOfParagraph:;
"^k" = deleteToEndOfParagraph:;
"^l" = centerSelectionInVisibleArea:;
"^v" = pageDown:;
"^t" = transpose:;
"^y" = yank:;
"^o" = (insertNewlineIgnoringFieldEditor:, moveBackward:);
"^P" = moveUpAndModifySelection:;
"^N" = moveDownAndModifySelection:;
"^B" = moveBackwardAndModifySelection:;
"^F" = moveForwardAndModifySelection:;
"^A" = moveToBeginningOfParagraphAndModifySelection:;
"^E" = moveToEndOfParagraphAndModifySelection:;
"^V" = pageDownAndModifySelection:;
"~^b" = moveWordBackward:;
"~^f" = moveWordForward:;
"~^B" = moveWordBackwardAndModifySelection:;
"~^F" = moveWordForwardAndModifySelection:;