BJT amplifier with differential input and negative feedback - Open loop analysis
Think about what the open-loop vulnerability of the circuit is if the voltage in the purple box below changed a tiny amount: -

I calculated the voltage (0.656 volts) from assumptions on other voltages in your circuit but, if I am out by a couple of milli-volt (and I surely will be) then how much will that change Q3's collector current.
You are expecting perfection when running open-loop and this won't happen (simulation or reality) - when you are closed-loop, the DC quiescent voltage at the output might be within a few milli-volts of 0 volts BUT, it won't be 0 volts. The voltage will be close but not exactly 0 volts. So, when you tie R6 to 0 volts (opening the feedback loop), you will get a massive shift in quiescent conditions due to the open loop gain of over 1000.
Put R6 back into close-loop and inspect the voltage at the output. Then use that DC voltage to feed the right-hand side of R6. It then should be much closer to what you expect.