Maybe use 555 output to CD4040 / 4060 to extend out to 20 seconds, then into a CD4017. First output pin on 4017 is to your flashing LEDs, second pin to beep circuit. No clue if this will work, just a whim from a hobbyist who likes things that light up (intentionally & unintentionally lol). But that's where I would start, since I have a bunch of said ICs and support components at hand.