How can I make due date more prominent on my card?

A good way of enlarging the due date is to increase the card font size. This way all the information is more visible.

To enable larger fonts on your cards, please go to Settings - Power-Ups - Developer Tools and open the blue link to scripts on Github.
From there, please choose the Large Font Script, copy its link, and paste it back in the Developer Tools dialogue box. Just click the plus icon, paste the link and Save Changes.
This will increase your closed card fonts.

You can also show full due dates directly on card fronts. This is possible via the Task Summary power-up. Feel free to go to Settings - Power-Ups - Task Summary to enable due dates, or any other card field, to show directly on a closed card.