I thought the main story doesn't give a sense of urgency because of the tadpole is basically dormant.
Make it so your party members starting to turn into mindflayer, one by one, if the player takes too long in the quest (or x amount of quest/rest). Eventually, you will turn into one yourself if you basically take forever doing ever quest.
With that said, give them the option to go back and finish their quest. Just don't allow players roam around and ignore the padpole completely.