I tried to search for reviews on it to see the plastic thing, but very few only found one pic of the back of your mobos, the only thing that i see is at the bottom of the pic
I had a similar issue when i was building MiniMi, but was very little what touched, so little that the bracket still sat down just it touch it, i gamble with it and still installed it, and working fine, but that was my risk to take, this is up to you, probably best to return it and get another cooler,
There is a 3rd mounting bracket for the AXP 140 thats its only 1156 (same as 1155), im guessing if you are right about the top one being 775, when 1156 was released they also released this mounting bracket so old AXP140 owners could move to 1156, im not sure if its still available, but you can check with your dealer, AXP-140 1156 Bolt-Thru-Kit
, from the description on thermalright webpage,
For Socket 1156 motherboards
For Thermalright AXP-140 and COGAGE MST-140. Also compatible with Thermalright Ultra Series, Venomous Series, Silver Arrow, Archon.
The one that came with my 2x HR02 and AXP 140 were, Venomous BTK
In my bracket, you need to set the screws in 2nd slot for it to install on 1155, the 3rd is for 1366, therefore leaving some space on the metal bracket till it finishes, depending on how much you could dremell it if it doesn't compromise the bracket, or use your washers but that will recess it to the inside of the case.... might even touch the back of the mobo (i would be careful with metal washers as it might short something), but maybe plastic washers... But if you can return it i would go that route and get another cooler, for me was not an option, returning it would be even more expensive than the heatsink itself. Or another option would be to return the mobo and go with one that could fit the AXP 140.