No, the hood shouldn't have to come all the way off.
As for the chain, he means put a chain across the engine and put a bolt into one of the accessory holes on the front of one head and the back of the block on the other to lift the engine with. Personally, I'd get a lift plate. You take the carb off, bolt the plate down and just put the hook from the engine hoist into one of the three holes.
Only reason a floor jack won't work is you're taking the oil pan off, so you can't lift it by that. Plus, while the engine crossmember is out you need to continue lifting the engine. You could use a floor jack to remove the old engine crossmember and install the new DIY one, then take the center piece back out but you said it's a no go on that upgrade for now. It shouldn't be too bad for you either way.