Update: After following your advice, I increased the water to 2 parts sugar and 1.5 parts water. The Demerara syrup worked! So thanks for that! Unfortunately, I forgot to account for the increase when remaking it, and it ended up tasting like straight Bourbon, for the most part.

It's the impurities in the sugar causing the issue but they also add to the flavour. The amount of water you will need to add will vary according to your sugar but perhaps try 2 sugar to 1.25 water or 1.5 water. (You will also need to adjust the cocktail recipe accordingly.) I use Monin's muscovado/demerara sugar as equivalent to 2:1 without the faff.

Any guidelines for the ratio then? Also, I did fine strain, but it was still clumpy and granular even after passing through the fine strainer. Meanwhile I got proper syrup without fine straining when it came to white sugar, so I am perplexed.

Sounds like the sugar you used. Dark sugars are always more problematic that more processed white sugars. You may have to slightly up the water ratio. Also, be sure to fine-strain syrup into store bottle as even tiny crystals will act as a catalyst to start crystallisation in the bottle.