Sten semi automatic rifle

Unless you can combine a simple blow back with a long recoil. i.e. the mass to be blown back includes the barrel and receiver. Still a lot of energy to be quickly absorbed even then.

Simple blow back combined with recoiling barrel takes us far away from just simple blow back, both in design and manufacture pase. There needs to be a mechanism to separate the recoilng parts one from another, plus another spring that will return barrel on it's place. Also make sure that barrel is well 'anchored' to the non-moveable parts of the rifle.
At any rate, people were making such weapons, especially in artillery, just we will probably see a non-STEN semi auto as a result here, not the STEN semi auto.

Does the recoiling barrel add to second shot control problems?

That probably depends on how the designer did it's job, both in concept and execution?
 
Unless you can combine a simple blow back with a long recoil. i.e. the mass to be blown back includes the barrel and receiver. Still a lot of energy to be quickly absorbed even then.
That's not blowback anymore--that's a recoil action. There's a good reason recoil action doesn't get used much in long arms outside of heavy machine guns: 80% of your operating mechanism is exposed and thus vulnerable to jamming, and large masses moving around (especially if you use tilt-locking) isn't good for accuracy.
 
Now the Austrians even made a blowback machine gun, the the Schwarzlose, and the British Kynoch company made a version of it in .303
A toggle-delayed blowback machine gun, which is a whole different animal.

I seem to remember that the rule of thumb is that for a full power cartridge in plain blowback you will need around 4 to 5 kilos of bolt mass, which would make for a rifle with daunting heft and some odd recoil characteristics. Might be plausible in a machine gun where you can fire off an open bolt without issues.
 
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