Creating slabs seems to be pretty straightforward: my issue/question is how do I make sure that my mods slabs that already exist in a world which is updated to 1.13.2 don't disappear because the game can't find them any more. Is it just a question of making sure the registry name stays the same?

Have a look at 

net.minecraft.util.datafix.fixes.ItemStackDataFlattening

There you can see how the items and their metadata are mapped to their flattened names.

Here is a little snippet from the file:

p_209282_0_.put("minecraft:sapling.3", "minecraft:jungle_sapling");
p_209282_0_.put("minecraft:sapling.4", "minecraft:acacia_sapling");
p_209282_0_.put("minecraft:sapling.5", "minecraft:dark_oak_sapling");
p_209282_0_.put("minecraft:planks.0", "minecraft:oak_planks");
p_209282_0_.put("minecraft:planks.1", "minecraft:spruce_planks");

I'm not sure how you would implement your own DataFix.

Here is a thread with the same problem: