I had three which would qualify as 'take downs' in my teens:
...An AR7 (like yours) but slightly earlier 70's variant, which stowed action and barrel into a hideous multi-coloured plastic stock.
...A winchester 1898 .22LR pump, which had a thumb screw on the left of the action that allowed you to detach the stock.
...and Dad had a broom handle Mauser in 9mm with a clip on stock which you could keep the whole pistol in like a wooden holster.