Well, the cabinet plans intend for the use of 3/4" MDF, so the you're probably going to have to double up the entire length, then a 3rd layer above the cabinet to match the 1.5" thickness.
And if you want to reduce resonance, you can use a product like Decidamp between the two main layers, since it also works as an adhesive, as well as an elastomer for constrained layer damping.
Then use regular wood glue on the upper, 3rd layer, & norez inside the cabinet.
I'd also made sure to probably use a 1/2", or larger, radius on the inner back side of the front baffle for the woofers, to help compensate for the added thickness.
But keep in mind that if the remaining parts of the cabinets should also be made using 1" of plywood (using the Decidamp between the doubled layers if still using the 1/2" plywood) and you'll have to make adjustments to the plan's given measurements, to make sure all parts match up.