Doublewing11 - have you considered RPG's Flutter Free product found here: http://www.rpginc.com/products/flutterfree/index.htm ? It is 1 1/16" deep which would appear to meet your 1"depth requirement. However, and this might be a deal breaker for you, it really is only effective over 2 octaves from 5kHz-20kHz as per RPG's calculated diffusion coefficient claims.
If all you want to do is kill some flutter echo's then this product will likely suffice as flutter echos tend to be more easily heard in the upper frequencies. But, if you wish to add spaciousness, source width and listener envelopment, then a 1" depth is totally inadequate; aim for 8"-12" or deeper yet to bring the effectiveness down to your room's transition (or Schroeder) frequency, which is likely about 300Hz for residential rooms.
Let us know what you're thinking or planning and perhaps others will chime in with sage advice.