12T Corncobs are available on E-Bay.
11T DNP Epoch is readily available (with the caveats above).
There are quite a few choices.
Think of gearing as a percent change. So, going from 13T to 12T = about 8% change.
13T to 11T = about a 17% change.
On the other end, 52T x 1.08 = 56T (equivalent of 13 to 12)
52T x 1.17 = 60T. (equivalent of 13 to 11).
And you get into mighty large chainrings very quickly.
Going from say 52T to 54T is only a 4% change, or half what you would get by dropping a single gear in the back.
You also have to start considering front and rear derailleur capacity, and the small front sprocket as you start going bigger up front. With some luck, it should still be able to handle it, but depending on the ultimate choice of components, it can be tight.