Ok. Thought about it. Here's my guess.

Before your throttle cable snapped, it was on its way out, either stretching of slipping. This caused the throttle plate to open less than it needed to for conditions. With less air being sucked through the carb, the needle would raise less and give you a leaner mix. Causing misfiring.

When the cable snapped, the throttle plate shut to the base idle position determined by the srop screw. Putting on a load at idle without increasing fuel and therefore revs would cause a stall. However you compensated by pulling out the choke and richening the fuel enough to increase revs and power to get you home.

Changing the cable fixes your problem. Though you'll have to check idle speeds.

Your plugs are probably ok. Though you could check.

How easily adjustable is your carbs fuel mix?