You are confusing a few things (as does your youtube). First, you need to distinguish between bias currents and offset current. The offset current is simply the difference between the two bias currents. If the offset current is significantly lower than the bias current, it says that the two bias currents are pretty much the same. If you look at the youtube, however, you'll see that the max bias current is listed as 100 pA, while the max offset current is 200 pA. In other words, there is no way to compensate since there is no way to tell exactly how the two bias currents will compare (the youtube guy got lucky).
In your case, though, you have an advantage. The independent bias currents which make offset current compensation difficult is characteristic of MOSFET op amps, while bipolar op amps do have correlated bias currents - and you are using a bipolar op amp. Please check the data sheet under Electrical Characteristics. For the TL972 the currents do correlate pretty well, so you can add a compensation resistor and expect some improvement. If you are going to do this, though, you need to calculate your parallel resistance correctly - in this case it is about 42k, not 140k. While you have done this and don't like the results you got, that does not change the fact that that's about as good as you're going to get. All this says is that the problem lies somewhere else, and fiddling with the compensation resistor will not help you understand it.
Once you've done that, though, it seems clear that you have missed the larger point of the youtube - offset voltage. Watch it again, and you will see him calculating the effect of Vos (input offset voltage) as Vos times the gain of the circuit. In your case, your gain is 10. And again, if you will read the data sheet, you will see that the max offset voltage is 6 mV. Multiply by 10 and you get a 60 mV output offset.
There is another possible error source which you need to check. Your scope offset controls may be contributing to the problem. Ground both inputs, and check to see what the scope is telling you the voltages are. Adjust the offsets to get exactly zero volts on both inputs, then recheck your measurements.
Nonideal opamps have input bias current - that is, they source or sink a small amount of current from their inputs. If you look at the LT6202 datasheet, you can see that for this opamp, with Vcm at half-rail voltage (which is roughly the case here), bias current will be between -7 and -1.3 microamps. This is sourcing current into your resistor divider and affecting the setpoint, equivalent to having a smaller resistor in the top half of your divider.
You can use lower value resistors to reduce the error - at the cost of more wasted current - or find an opamp with smaller input bias current.
Best Answer
The bias is typically set at half the supply voltage (in solutions without bipolar power supplies) because that puts it the farthest from clipping against either rail. You can adjust it up or down if you want, but the closer it gets to one rail the smaller the permissible signal variation in that direction.
Since most audio signals are symmetrical, moving it in either direction away from the midpoint reduces the maximum signal amplitude.