How to overcome the limits (they are not god given nor the end of the line......)

To understand how to measure lower THD, you must know how the AP2 analyzer works (in general)

First, you must detect, that the oscillator and or the preamp is the limiting element, not the notch (you can see it on the FFTs)

AP2 oscillators FFT after notch (1kHz)
(k2 has -127 dB -> 450nV, k3 has 132 dB -> 250nV, Noise is 150dB * 141.4 -> 4.5µV --> 5,2µV -> ~ 106dB)

But how to supress k2 (thats even bigger than k3) to test if the Oscillator or the preamp is the problem ?
Build an active RC lowpass with 1kHz is a solution.
You will loose 3dB of gain @ 1kHz, but that doesn't matter because THD(+N) is a ratio measurement....
With a 2nd order Lowpass you will win ~12 dB/octave and what's an ocatve ? Right, the distance from 1kHz to 2kHz is an octave !
So you will supress k2 (2kHz) by approx 10-12dB (all parts are not that low tolerance :-) and k3 (3kHz) by approx 15-18dB.
That will give more room down to ~ 125-130 dB @ 1V,1kHz

If you would go even further, build a 4th order lowpass...................

But never (and really never) treat the instruments so far below any conventional level....
Before treating the THD(+N) display, have a look into the FFT, because you will see if the Noise floor  is the only thing you measure
or your low pass isn't connected (can happen in the middle of the night :-)

If you have succesfully removed the k2 and k3, you must check in the FFT, if the signal is supressed enough, else you can estimate THD only by adding all harmonics....
If there are no harmonics anymore but you can see the signal, you must add another notch to supress signal further.
(But then, you are at approx. -140dB THD and should think about a new measurement system or to go out and have some fresh air)
Double check every measurement by changing the frequency well below your LowPass Filter to see if your circuit is working anymore :-)

Tip #1:      If averaging the FFT N-times, you will lowering the Noise Floor by N
Tip #2:      The THD (without +N) will analyze ONLY the harmonics, not the Noise
Tip #3:      The THD+N will measure the voltage after the notch filter for the fundamental (also Noise, hum,....)
Tip #4:      Use a DC sypply wich GND is not connected to earth.
Tip #5:      Move your circuit, all cables and the measuring instrument (including all external fiilters !) far away from magnetic and electric fields.
                 You will be in a region (Noise and THD) were the fluorescent lamp can introduce noise and unwanted signals, even if it is in the next room !
                 If you measure 126 dB SNR at 1V level, the instrument will measure 1µVrms only !
Tip #6:      Only use clean boards (old solder flux can make high impedance connections)
Tip #7:      Only use good cables (with defective or only sometimes defective cables you would only search errors where are none)
Tip #8:      Use shielded and differential cables wich are as short as possible
Tip #9:      Repeat unbelievable measurements many times until they are repeatable. Check with other frequencies/levels that your circuit is working anymore.
Tip #10:    Be carefull with datasheet diagramms or results ! They are only valid in a given circuit under given parameters ! (gain, voltage, load, ......)
                 In some cases, it's difficult to extrapolate it to other circuits or parameters !
Tip #11:    At some point in the development, you must decide between high SNR, low THD and usability
                 (an input impedance of 10 Ohms seems not to be usable for most available opamps wich must drive it)
                 also lower resistance values decrease noise but will increase current flow and therefore THD