I have a 180g tank with a composite dirt bottom capped with gravel. I.e. Miracle Grow Organic potting soil, Clay, Powdered Charcoal, etc. The Hayward EC40 is the only mechanical filtration I am currently running. I need to redo my overflow at which time I will add some pre-filtration to remove large sentiment before it makes it to the EC40. When I brought up this tank it took about 3 hours for the water to go from mud puddle to perfectly clear. That initial charge when bringing up the tank lasted about a month before I had to change it out.
I just had to change out the DE in the EC40 a couple days ago after running the charge of DE for 3 months. This is without any pre-filtering and doing a fair amount of landscaping which kicks up the fine clay particles into the water stream.
The EC40 is made to filter pools of many thousands of gallons (It is rated for pools up to 19,200g). My recollection is the screen area of the EC40 is 40 sq ft . Once the screens are coated with DE the actual surface area of the DE is many times that which is the advantage of the unique properties of Diatomaceous Earth. My best educated guess is that the EC40 would handle your 1100g tank/sump pair without issue and my best guess is that you should be able to easily get 3 months out of a charge of DE since you aren't running a dirt bottom (I believe?).
I have used this EC40 with pumps as small as a Quiet One 4000 on a 35g hex tank to as large as my current Jeboa 20,000 on my current 180g. They all have worked very well for me.
Here is an old picture from when I was setting up the tank:
View attachment 1469977
The output of the EC40 goes through a shutoff valve, one way valve to a 2 output T valve. When I recharge the DE I switch the T valve to by pass the tank and dump the output of the EC40 directly back into the sump. Once the EC40 has been charged and the water coming from it is clear (less than 5 minutes) I switch the T valve to push the water output from EC40 into the main tank via bottom returns.
I know there are a lot of pages in the thread linked to in my signature, I have been running the EC40 for 10 years now.
I believe you can setup the EC40 so you can backwash the DE out of the filter instead of taking it apart but I have never tried it in this configuration.