It is possible to target specific frequency range and absorb radiation using EBG arrays etched on a FR4 substrate. There are plenty of papers with various configurations, with and without chip resistors. Such PCB can replace the top cover of the aluminum shielding enclosure. I did some simulations few years ago and I remember that 1.6mm FR4 was good frequencies 10GHz and lower, and 1.0mm FR4 for 20GHz and higher. Substrate height directly influences via height, so to create optimal absorptive "mushroom" need to choose via diameter, substrate thickness and patch size. There are some pros and cons, and of the problems is that with a large number of EBG elements via count can add to the cost. Via-less EBG structures are usually not very robust, but maybe there are some good configurations. For example, absorptive element created using two radial stubs with a chip resistor in-between, or something like that.