How can I use molasses without making a mess?
Try slowly twisting the jar as you slow down your pour. This is what I do and it works pretty well.

This is actually something you'll see waiters and bartenders do when pouring wine, too. This video shows the action at around 3:20 in. 

Twisting the bottle causes the drip to collect on the inside of the rim and keeps it from dripping down the side. Because the molasses is more viscous than wine, it may take a bit more turning but it does work well.