You have to keep in mind that attenuation and absorption are not to be used interchangeably!
As Tetsujin states in their comment, the foam won't do much, as it may attenuate the sound in a "statistical manner". This means that the sound will have to interact with the material for quite some time but what you are interested in is to block the sound from going through the material.
In general and in the simplest way, this happens with mass! By adding mass on the boundary you increase the amount of energy that reflects from the surface (you create a greater impedance mismatch at the interface). So, as a rule of thumb, the heavier the material you will use the better the attenuation in the adjacent room will be.
A different approach would be to introduce more than one interfaces. Simply stated, use many different materials. The calculation of the total attenuation is not trivial to be done but if you use some foam in between the rest of the materials the result can be quite satisfactory, especially for the mid to mid-high and high frequencies. Keep in mind that you should not expect much for the low frequencies (200-300 Hz is already too optimistic to set as a low-frequency target), as you would require A LOT of mass to stop those frequencies from going to the adjacent room.
Finally, you could also try to "isolate" the panel from the adjacent boundaries to avoid flanking transmission in the panel, but I believe that this would provide unnoticeable results as most of the sound will anyway continue in other flanking paths towards the adjacent room.