I'm fortunate the bridge and trem are stable on my pre-CBS '65. I'm not much of a technician, maybe because I haven't had to be. But I do know a stringing trick I learned on acoustics that works well on my electrics, regardless of whether the post is slotted or has holes.
1. Draw the string taught from the bridge and wrap it around the post twice, from the bottom of the post up;
2. Keeping tension on the string, slide it down into the slot;
3. Keeping the tension on the string, turn the key till you bring the string to pitch.
This locks the string around the post. This type of lock eliminates breaks caused by locking the string against the edge of the slot.
By the way, stringing an electric is a bit more complicated than stringing an acoustic, and I know acoustic pickers who pay the guitar shop to change their strings. That seems silly to me...keep learning how to string your axe. It's like knowing how to check the oil in yer car.