I recently came across this 2c Washington in a feeder album that has really stumped me--hopefully someone can help me identify it. Normally I don't have too much difficulty with parsing these issues out except for sometimes the watermarks, but this one is resisting my efforts.
I'll start by listing all its characteristics:
1. Perforated 11 horizontally
2. Rotary press (determined by comparing to a known flat plate)
3. Type I die
4. No discernible watermark
You may quickly start to see that something isn't adding up here... The stamp was placed in the spot for #411, but we know that is incorrect right off the bat since #411 is perf 8.5.
As far as I know, there weren't any coil stamps perforated 11, so my first thought was that somebody trimmed down a regular stamp to make a fake coil. But this doesn't work out since the only perf 11 2c Washington rotary press is #546, which is a Type III die. We run into the same issue even if someone trimmed down a coil waste #539 or #540, being Type II and III dies, respectively.
So, what am I missing here? I'm at a loss. The closest I could come to is that it's a trimmed down #540 and I am just misidentifying the die type--my mystery stamp fits all the other characteristics--but I really don't think that is the case.
I've tried to attach photographs of everything as best I can, including the comparison to a flat plate stamp, multiple perf measurements, and a magnified shot of the details to determine die type. Hopefully they show up well enough at the tiny size I have to upload them at on this site.

Front View

Back View

Comparison to flat plate

Closeup of the detail for die type

More closeup details

Upper perf measurements

Lower perf measurements

Additional perf measurements.