Unfortunately regular photo gloss, satin and matte is the only large format we can print on, it's not as thick as card stock.

To understand this, it helps to know how most large format printing works - it's done on large inkjet printers that use rolls for the source media. Thick stock like cardstock, etc cannot be 'rolled', making large format printing difficult. Thick stocks are usually done on small offset presses. If you did need large format on a thick stock, this would require a large flat bed printer and that is quite an expensive process - you'd have to search for something like "flat bed printing" and most likely it would be done by a local sign shop.