Interesting gun in those pix.
I'm just a layman not a gun expert, so don't put too much reliance in what I'm saying here, but here's what I think.
I'm not sure your gun should be called a Model 11.
Lets review some history: John Moses Browning patented his autoloading shotgun circa 1898. Fabrique Nationale of Leige, Belgium was granted the rights to manufacture and market Brownings patented shotgun for the European market after about 1902. (We call their gun the A-5.) I'm not sure why FN didn't get the rights to sell the gun in the US too, but they didn't.
Instead, Remington was licensed to manufacture and sell Brownings patented shotgun in the US, but not until 1905. Remington originally called their gun the Remington Autoloading Shotgun, not the Remington Model 11. They made a few minor changes to the gun in 1911 and their gun was ever afterward called the Model 11, which was shorthand, meaning the Model of 1911. I think those changes may have just been cosmetic; a flying duck rollmark on one side of the receiver; a flying pheasant on the other side of the receiver, and MODEL 11 rollmarked into the breechbolt.
I have also read somewhere that sometime between 1902 when FN started European production and 1905 when Remington began production in the US, Fabrique Nationale directly supplied John M. Browning 5000 of the guns they made in Belgium so that he could sell them himself to the US market, which he supposedly did from his Ogden Utah location. I don't know if those 5000 guns were just A-5's they diverted from the European market, or whether they made a special run of unmarked guns for Browning to sell in the US. My guess is that they were unmarked and that FN had agreed to do this as part of the price they paid for obtaining their license to manufacture the gun for the European market. Maybe John Browning originally wanted to sell his shotgun to the US market himself, or at least wanted to do so for long enough to leverage Remington into giving him what he wanted for the rights to make and sell the gun here, which was a percentage of every gun sold.
This brings me back to your particular gun. First off, I don't know if the wood furnishings on your gun are original or not. The wood may be original but refinished but my guess is its all aftermarket. They sure don't look like the wood furnishings on my Remington Model 11 that was manufactured in 1938. The shape is right, but the color is different and there is no checkering on your guns forearm or pistol grip. Again, this may have just been a feature of pre-1911 guns, I don't know, but the stock and forearm don't look worn at all which is hard to believe in a gun of that age with the reputation Model 11's have for cracking stocks and forearms.
There are no duck or pheasant rollmarks on your receiver and there is no MODEL 11 rollmark on your breechbolt.
The suicide safety in front of your trigger is from 1928 or earlier (this was changed in 1928. Guns manufactured after that had button safetys on the side of the receiver behind the trigger) so, it would appear that the receiver portion of your gun and presumably all its other metal parts are at least that old.
However, your receiver looks like its been refinished relatively recently, which complicates things.
Bottom line, there appear to be only four possibilities:
1. The receiver (at least) is either from the 5,000 guns shipped from Leige Belgium to John Browning sometime between 1902-1905, OR
2. The receiver (at least) was manufactured by Remington between 1905-and 1911 as part of a Remington Autoloading shotgun they made in the years before they added rollmarks to receiver and breechbolt and renamed the gun the Model 11.
3. The gun was a Model 11 manufactured sometime between 1911 and 1928 but the rollmarks were ground off both the receiver and the breechbolt before refinishing the gun.
4. There's something I don't know.